GMM - trials.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pd.options.display.max_rows = 4000\n",
    "pd.set_option('display.float_format', lambda x: '%.2f' % x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv('../../0.Data/1.Interim/New/current_cluster.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import zscore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df_.drop('cust_bhvr_scr_nbr', axis = 1, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['MOBILITY_REGION_NAME_flagCentral', 'MOBILITY_REGION_NAME_flagEast',\n",
       "       'MOBILITY_REGION_NAME_flagWest', 'ACCT_STS_AT_CALL_DATE_flagN',\n",
       "       'ACCT_STS_AT_CALL_DATE_flagO', 'ACCT_STS_AT_CALL_DATE_flagS',\n",
       "       'TOT_DUE_AMT', 'Promise_%', 'A_avg', 'P_avg', 'ar_bhvr_scr_nbr',\n",
       "       'avg_paid_full_dy_cnt', 'cust_recls_scr_nbr', 'wirls_ln_cnt',\n",
       "       'excpt_ovrd_ind', 'pyarr_scr_nbr', 'lst_bhvr_scr_nbr',\n",
       "       'preferred_month_CALL_DT', 'preferred_day_of_monthCALL_DT',\n",
       "       'preferred_weekdayCALL_DT', 'return_itm_180_dy_cnt',\n",
       "       'return_itm_30_dy_cnt', 'Tenure', 'mthd_total', 'MA_%', 'CC_%',\n",
       "       'DD_%', 'ME_%', 'ML_%', 'CK_%', 'EF_%', 'src_total', 'APP_%',\n",
       "       'IVR_%', 'KIO_%', 'REP_%', 'SMS_%', 'WEB_%', 'prms_outcome_total',\n",
       "       'BRKPROM_%', 'DELPROM_%', 'KPTPROM_%', 'OPEN_%', 'RNGPROM_%',\n",
       "       'init_outcome_total', 'TKNPROM_init_%', 'RNGPROM_init_%'], dtype=object)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_ = df.apply(zscore)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(377122, 48)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Run GMM \n",
    "from sklearn.mixture import GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[51371043.040718064,\n",
       " 32503810.008622553,\n",
       " 22245160.259867154,\n",
       " 10439388.236651605,\n",
       " 11206846.194081439,\n",
       " 9809228.3093076181,\n",
       " 5893338.794090189,\n",
       " 3403641.8695234349,\n",
       " 3120761.1627317807]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "aic.append(3120761.1627317807)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13\n"
     ]
    }
   ],
   "source": [
    "for k in range(10, 14):\n",
    "    gmm = GMM(n_components=k).fit(df_)\n",
    "    aic.append(gmm.aic(df_))\n",
    "    print(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13\n",
      "CPU times: user 49min 28s, sys: 9min 50s, total: 59min 18s\n",
      "Wall time: 19min 48s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "bic = []\n",
    "for k in range(1, 14):\n",
    "    gmm = GMM(n_components=k).fit(df_)\n",
    "    bic.append(gmm.bic(df_))\n",
    "    print(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(aic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from sklearn import metrics\n",
    "from scipy.spatial.distance import cdist\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k = [1,2,3,4,5,6,7,8,9,10,11,12,13]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5893338.794090189"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aic[6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "911611.41981022817"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bic[6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HwuRgIiIirdGWwLEvcHUz918D/Lp95UgS7LADnHoqnHEGPPts7GpERCQJ2hI4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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9dd534b780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the elbow\n",
    "plt.plot(k, aic, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('AIC')\n",
    "plt.title('The graph shows AIC value w.r.t. k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Z2Y/M7Awz+2nOoY4kvsE82r6vTNpTZsxG7s9HA++0Z9gQEZFlS12XSmZk+DSi2XEYMb5i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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9dd4e08be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the elbow\n",
    "plt.plot(k, bic, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('BIC')\n",
    "plt.title('The graph shows BIC value w.r.t. k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VpxRTv35w7rnhHkAzZ8YdjYgUSomKSMLU16s+pdh+9jPo3TvcXVlEKosSFZEE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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9deab44b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the elbow\n",
    "plt.plot(k, diff, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('AIC - BIC')\n",
    "plt.title('Difference between AIC and BIC value w.r.t. k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "diff = [0]\n",
    "for i in range(0,12):\n",
    "    diff.append(round(aic[i+1]-bic[i+1],2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/opt/app/anaconda2/python36/lib/python3.6/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 47s, sys: 15.7 s, total: 2min 3s\n",
      "Wall time: 26.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gmm = GMM(n_components=6).fit(df_)\n",
    "labels = gmm.predict(df_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_w_label = df_.copy()\n",
    "df_w_label['lbl'] = labels "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-959594.44330965623"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aic[10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1305351.8248615013"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bic[10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df_test = df_.head(50000)\n",
    "labels_test = labels[0:50000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.067128670217129954"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silhouette_score(df_test, labels_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "377122"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df_test = df_.head(50000)\n",
    "labels_test = labels[0:50000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.067128670217129954"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silhouette_score(df_test, labels_test)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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