PCA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis (PCA) of Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ja/miniconda3/envs/gds/lib/python3.6/site-packages/numpy/lib/arraysetops.py:522: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  mask |= (ar1 == a)\n"
     ]
    },
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>business2016</th>\n",
       "      <th>pop2016</th>\n",
       "      <th>emp2016</th>\n",
       "      <th>int3way</th>\n",
       "      <th>int4way</th>\n",
       "      <th>walk_edge_length</th>\n",
       "      <th>transit_n_per_hour</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hexid</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th>910309</th>\n",
       "      <td>1.066477</td>\n",
       "      <td>17.449574</td>\n",
       "      <td>4.574052</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1310416</th>\n",
       "      <td>0.044870</td>\n",
       "      <td>1.991111</td>\n",
       "      <td>0.593479</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>369.275908</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         business2016    pop2016   emp2016  int3way  int4way  \\\n",
       "hexid                                                          \n",
       "910309       1.066477  17.449574  4.574052        0        0   \n",
       "2291575      0.002350   0.015851  0.025705        0        0   \n",
       "2400369      0.039452   0.514006  0.049109        0        0   \n",
       "1488598      0.751256   8.662247  2.462499        0        0   \n",
       "1310416      0.044870   1.991111  0.593479        0        0   \n",
       "\n",
       "         walk_edge_length  transit_n_per_hour  \n",
       "hexid                                          \n",
       "910309         423.237908                 0.0  \n",
       "2291575          0.000000                 0.0  \n",
       "2400369          0.000000                 0.0  \n",
       "1488598          0.000000                 0.0  \n",
       "1310416        369.275908                 0.0  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# load in the data\n",
    "\n",
    "df = pd.read_csv(\"output_hex_data/out_data_hex_all.csv\",index_col=\"hexid\")\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scale the data\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "features = ['business2016', 'pop2016', 'emp2016', 'int3way', 'int4way', 'walk_edge_length', 'transit_n_per_hour']\n",
    "\n",
    "# Separating out the features\n",
    "x = df.loc[:, features].values\n",
    "\n",
    "# Standardizing the features\n",
    "x = StandardScaler().fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.388671</td>\n",
       "      <td>-0.209911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.527194</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>0.196152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.359707</td>\n",
       "      <td>0.276839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
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      ],
      "text/plain": [
       "          0         1\n",
       "0  0.388671 -0.209911\n",
       "1 -0.527194  0.193631\n",
       "2 -0.518888  0.196152\n",
       "3 -0.359707  0.276839\n",
       "4  0.037515 -0.257234"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "\n",
    "principalComponents = pca.fit_transform(x)\n",
    "\n",
    "principalDf = pd.DataFrame(data = principalComponents)\n",
    "\n",
    "principalDf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(x)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('Number of Components')\n",
    "plt.ylabel('Variance (%)') #for each component\n",
    "plt.title('Dataset Explained Variance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import FactorAnalysis\n",
    "\n",
    "transformer = FactorAnalysis(n_components=2, random_state=0)\n",
    "X_transformed = transformer.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.29483069],\n",
       "       [-0.30519388],\n",
       "       [-0.30073776],\n",
       "       ...,\n",
       "       [-0.30542117],\n",
       "       [-0.30542117],\n",
       "       [-0.30542117]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_transformed"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}