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notebook.tex
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% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{jnmf-experiment}
% Pygments definitions
\makeatletter
\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
\let\PY@ul=\relax \let\PY@tc=\relax%
\let\PY@bc=\relax \let\PY@ff=\relax}
\def\PY@tok#1{\csname PY@tok@#1\endcsname}
\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
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\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
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\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
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\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}}
\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}}
\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@fm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
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\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
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\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@dl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\def\PYZbs{\char`\\}
\def\PYZus{\char`\_}
\def\PYZob{\char`\{}
\def\PYZcb{\char`\}}
\def\PYZca{\char`\^}
\def\PYZam{\char`\&}
\def\PYZlt{\char`\<}
\def\PYZgt{\char`\>}
\def\PYZsh{\char`\#}
\def\PYZpc{\char`\%}
\def\PYZdl{\char`\$}
\def\PYZhy{\char`\-}
\def\PYZsq{\char`\'}
\def\PYZdq{\char`\"}
\def\PYZti{\char`\~}
% for compatibility with earlier versions
\def\PYZat{@}
\def\PYZlb{[}
\def\PYZrb{]}
\makeatother
% Exact colors from NB
\definecolor{incolor}{rgb}{0.0, 0.0, 0.5}
\definecolor{outcolor}{rgb}{0.545, 0.0, 0.0}
% Prevent overflowing lines due to hard-to-break entities
\sloppy
% Setup hyperref package
\hypersetup{
breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\begin{document}
\maketitle
Table of Contents{}
{{1~~}Imports and configurations}
{{2~~}The Data}
{{3~~}Standard JNMF}
{{3.1~~}Hyperparameters}
{{3.2~~}Results}
{{3.2.1~~}Classification by maximum filter}
{{3.2.1.1~~}Drug}
{{3.2.1.2~~}Protein}
{{3.2.1.3~~}Mutation}
{{3.2.2~~}Classification by z-score}
{{4~~}Integrative JNMF}
{{4.1~~}Hyperparameters}
{{4.2~~}Results}
{{4.2.1~~}Analysis}
\hypertarget{imports-and-configurations}{%
\subsection{Imports and
configurations}\label{imports-and-configurations}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}1}]:} \PY{k+kn}{from} \PY{n+nn}{lib}\PY{n+nn}{.}\PY{n+nn}{ToyMatrixClass} \PY{k}{import} \PY{o}{*}
\PY{k+kn}{from} \PY{n+nn}{lib}\PY{n+nn}{.}\PY{n+nn}{StandardJnmfClass} \PY{k}{import} \PY{o}{*}
\PY{k+kn}{from} \PY{n+nn}{lib}\PY{n+nn}{.}\PY{n+nn}{IntegrativeJnmfClass} \PY{k}{import} \PY{o}{*}
\PY{k+kn}{import} \PY{n+nn}{lib}\PY{n+nn}{.}\PY{n+nn}{datasets} \PY{k}{as} \PY{n+nn}{data}
\PY{k+kn}{import} \PY{n+nn}{plotly}\PY{n+nn}{.}\PY{n+nn}{offline} \PY{k}{as} \PY{n+nn}{py}
\PY{k+kn}{import} \PY{n+nn}{seaborn} \PY{k}{as} \PY{n+nn}{sns}
\PY{n}{py}\PY{o}{.}\PY{n}{init\PYZus{}notebook\PYZus{}mode}\PY{p}{(}\PY{n}{connected}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{k+kn}{import} \PY{n+nn}{plotly}\PY{n+nn}{.}\PY{n+nn}{graph\PYZus{}objs} \PY{k}{as} \PY{n+nn}{go}
\PY{k+kn}{import} \PY{n+nn}{cufflinks} \PY{k}{as} \PY{n+nn}{cf}
\PY{n}{cf}\PY{o}{.}\PY{n}{go\PYZus{}offline}\PY{p}{(}\PY{p}{)}
\PY{n}{cf}\PY{o}{.}\PY{n}{set\PYZus{}config\PYZus{}file}\PY{p}{(}\PY{n}{colorscale}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{spectral}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline
\end{Verbatim}
\hypertarget{the-data}{%
\subsection{The Data}\label{the-data}}
This is the small dataset comprising of the following different data. -
\texttt{DRUG}: Response of Cell line to Drug - \texttt{MUT}: Mutation of
Cell line (bool) - \texttt{PROT}: Amount of protein
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{x} \PY{o}{=} \PY{n}{data}\PY{o}{.}\PY{n}{small}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Imported DRUG with shape (39, 67)
Imported MUT with shape (39, 7)
Imported PROT with shape (39, 19)
\end{Verbatim}
\hypertarget{standard-jnmf}{%
\subsection{Standard JNMF}\label{standard-jnmf}}
The vanilla JNMF algorithm. The factors, \texttt{W} and \texttt{H1},
\texttt{H2}, \texttt{H3} have been averaged over the different
initializations (50 in this case) and then used for clustering.
\hypertarget{hyperparameters}{%
\subsubsection{Hyperparameters}\label{hyperparameters}}
\begin{itemize}
\tightlist
\item
\texttt{super\_niter} - number of different initalizations
\item
\texttt{niter} - number of iterations for one particular intialization
\item
\texttt{k} - number of clusters
\item
\texttt{thresh} - Threshold for z-score based clustering
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{super\PYZus{}iter} \PY{o}{=} \PY{l+m+mi}{50}
\PY{n}{niter} \PY{o}{=} \PY{l+m+mi}{100}
\PY{n}{k} \PY{o}{=} \PY{l+m+mi}{3}
\PY{n}{thresh} \PY{o}{=} \PY{l+m+mi}{0}
\PY{n}{m} \PY{o}{=} \PY{n}{StandardNmfClass}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{k}\PY{p}{,} \PY{n}{niter}\PY{p}{,} \PY{n}{super\PYZus{}iter}\PY{p}{,} \PY{n}{thresh}\PY{o}{=}\PY{n}{thresh}\PY{p}{)}
\PY{n}{m}\PY{o}{.}\PY{n}{super\PYZus{}wrapper}\PY{p}{(}\PY{n}{verbose}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Error:}\PY{l+s+si}{\PYZpc{}f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{m}\PY{o}{.}\PY{n}{error}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Error:0.658881
\end{Verbatim}
\hypertarget{results}{%
\subsubsection{Results}\label{results}}
\hypertarget{classification-by-maximum-filter}{%
\paragraph{\texorpdfstring{Classification by \textbf{maximum
filter}}{Classification by maximum filter}}\label{classification-by-maximum-filter}}
After comparing the results from NMF below with the the grouping we had
done manually from research, we've come to the following conclusions
about the various matrices.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{221}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{222}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{MUT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{223}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PROT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}4}]:} <matplotlib.axes.\_subplots.AxesSubplot at 0x104259358>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_9_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{drug}{%
\subparagraph{Drug}\label{drug}}
\begin{itemize}
\tightlist
\item
\textbf{Class 0}: Represents Chemotherapeutic drugs with the exception
of only two, `LY294002' and `PI3k-alpha'
\item
\textbf{Class 1 \& 2}: Represent molecular targeted drugs, with a
further split into `Akt' targets and others.
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}5}]:} \PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{n+nb}{list}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{index}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{iplot}\PY{p}{(}\PY{n}{kind}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{heatmap}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{colorscale}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{spectral}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\hypertarget{protein}{%
\subparagraph{Protein}\label{protein}}
This particular one doesn't give as accurate results as ``DRUG'' and
``MUT''. However, it seems like it classifies into the MAPK3 pathway and
the AKT pathway with the latter further subdivided into PI3k and AKT
pathway.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PROT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{n+nb}{list}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PROT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{index}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{iplot}\PY{p}{(}\PY{n}{kind}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{heatmap}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{colorscale}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{spectral}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\hypertarget{mutation}{%
\subparagraph{Mutation}\label{mutation}}
Here it clusters only into two groups even though the rank is 3. This
behaviour is observed even in multiple runs. Out of the two groups, the
gene ``PTEN'' is the only member of one group which makes sense as it is
a tumor-suppressor whereas the others are proto-oncogenes.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{MUT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{n+nb}{list}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{MUT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{o}{.}\PY{n}{index}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{iplot}\PY{p}{(}\PY{n}{kind}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{heatmap}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{colorscale}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{spectral}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\hypertarget{classification-by-z-score}{%
\paragraph{\texorpdfstring{Classification by
\textbf{\emph{z-score}}}{Classification by z-score}}\label{classification-by-z-score}}
Classification by z-score is done by subtracting each of the \texttt{H}
matrices with the mean of the entire matrix and dividing by the standard
deviation (basically normalizing) and grouping, if the particular value
is above a threshold.
This was modeled by
\href{https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5006236/}{Yang et al}
and was supposed to give better classification compared to max
filtering. But, I have not been able to get meaningful results.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}8}]:} \PY{k}{for} \PY{n}{v} \PY{o+ow}{in} \PY{n}{m}\PY{o}{.}\PY{n}{z\PYZus{}class}\PY{o}{.}\PY{n}{values}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{n}{v}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{n+nb}{list}\PY{p}{(}\PY{n}{v}\PY{o}{.}\PY{n}{index}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{iplot}\PY{p}{(}\PY{n}{kind}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{heatmap}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{colorscale}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{spectral}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\hypertarget{integrative-jnmf}{%
\subsection{Integrative JNMF}\label{integrative-jnmf}}
This is a new technique to perform NMF developed by
\href{https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5006236/}{Yang et al}
that provides a tighter integration between the datasets compared to the
standard JNMF
\hypertarget{hyperparameters}{%
\subsubsection{Hyperparameters}\label{hyperparameters}}
\begin{itemize}
\tightlist
\item
\texttt{super\_niter} - number of different initalizations
\item
\texttt{niter} - number of iterations for one particular intialization
\item
\texttt{k} - number of clusters
\item
\texttt{lamb} - Hyperparameter for I-NMF
\item
\texttt{thresh} - Threshold for z-score based clustering
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{super\PYZus{}iter} \PY{o}{=} \PY{l+m+mi}{50}
\PY{n}{niter} \PY{o}{=} \PY{l+m+mi}{4960}
\PY{n}{k} \PY{o}{=} \PY{l+m+mi}{3}
\PY{n}{lamb} \PY{o}{=} \PY{l+m+mi}{5}
\PY{n}{thresh} \PY{o}{=} \PY{l+m+mf}{1.3}
\PY{n}{m} \PY{o}{=} \PY{n}{IntegrativeNmfClass}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{k}\PY{p}{,} \PY{n}{niter}\PY{p}{,} \PY{n}{super\PYZus{}iter}\PY{p}{,} \PY{n}{thresh}\PY{o}{=}\PY{n}{thresh}\PY{p}{,} \PY{n}{lamb}\PY{o}{=}\PY{n}{lamb}\PY{p}{)}
\PY{n}{m}\PY{o}{.}\PY{n}{super\PYZus{}wrapper}\PY{p}{(}\PY{n}{verbose}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Error:}\PY{l+s+si}{\PYZpc{}f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{m}\PY{o}{.}\PY{n}{error}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Error:0.551361
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor} }]:} \PY{n}{k}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}
\PY{n}{a}\PY{o}{=}\PY{l+m+mi}{0}
\PY{n}{b}\PY{o}{=}\PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{k} \PY{o+ow}{in} \PY{n}{m}\PY{o}{.}\PY{n}{x}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{k}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{w}\PY{p}{,}\PY{n}{m}\PY{o}{.}\PY{n}{h}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{m}\PY{o}{.}\PY{n}{x}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{b}\PY{o}{+}\PY{o}{=}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{w}\PY{p}{,}\PY{n}{m}\PY{o}{.}\PY{n}{h}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{m}\PY{o}{.}\PY{n}{x}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{w}\PY{p}{,}\PY{n}{m}\PY{o}{.}\PY{n}{h}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{m}\PY{o}{.}\PY{n}{x}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{a}\PY{o}{+}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{abs}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{w}\PY{p}{,}\PY{n}{m}\PY{o}{.}\PY{n}{h}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{m}\PY{o}{.}\PY{n}{x}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{m}\PY{o}{.}\PY{n}{calc\PYZus{}error}\PY{p}{(}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{error}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{a}\PY{p}{,}\PY{n}{b}\PY{p}{)}
\end{Verbatim}
\hypertarget{results}{%
\subsubsection{Results}\label{results}}
After a few tweaks, the i-NMF algorithm gives much better and more
stable results compared to the standard JNMF.
The classification has been done by maximum filter. I believe maximum
filter is a better way of doing the classification compared to z-score
for this dataset. Z-score allows a particular feature to be part of
multiple clusters which wouldn't make sense for this dataset and
analysis.
Below, I've plotted the Consensus Matrix computed over 50 different
iterations. As you can see there is a high level of correlation with the
values being near binary.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{221}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{DRUG}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{222}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{MUT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{MUT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{223}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PROT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{heatmap}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class\PYZus{}cm}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PROT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}18}]:} <matplotlib.axes.\_subplots.AxesSubplot at 0x10d0f10b8>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_23_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{analysis}{%
\paragraph{Analysis}\label{analysis}}
Below, I've plotted the `H' matrices. Here, Class 1 contains the PTEN
mutation. Correspondingly all the proteins downstream to PTEN are
clustered in the same class. The akt and pik inhibitors are also
clustered in the same category.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{k}{for} \PY{n}{v} \PY{o+ow}{in} \PY{n}{m}\PY{o}{.}\PY{n}{max\PYZus{}class}\PY{o}{.}\PY{n}{values}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{n}{v}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{n+nb}{list}\PY{p}{(}\PY{n}{v}\PY{o}{.}\PY{n}{index}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{iplot}\PY{p}{(}\PY{n}{kind}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{heatmap}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{colorscale}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{spectral}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
% Add a bibliography block to the postdoc
\end{document}