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notebook.tex
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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{flink\_k-means}
% 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@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##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@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##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@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##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}}}
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\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@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##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@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
\expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}}
\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##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@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}}
\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##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@ch\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@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##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@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##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@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##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@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##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}}}
\expandafter\def\csname PY@tok@sa\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##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
\hypertarget{apache-flink}{%
\section{Apache Flink}\label{apache-flink}}
Implement the k-means clustering algorithm in Apache Flink.
Optional: implement the same algorithm in OpenMP/MPI and compare the
performance of the two implementations (processing time and scalability)
under various workloads.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}24}]:} \PY{k+kn}{import} \PY{n+nn}{csv}
\PY{k+kn}{import} \PY{n+nn}{random}
\PY{k+kn}{import} \PY{n+nn}{sys}
\PY{k+kn}{import} \PY{n+nn}{numpy}
\PY{k+kn}{import} \PY{n+nn}{os} \PY{c+c1}{\PYZsh{} We need this module}
\PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt}
\PY{k+kn}{import} \PY{n+nn}{seaborn} \PY{k}{as} \PY{n+nn}{sns}\PY{p}{;}
\PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{datasets}\PY{n+nn}{.}\PY{n+nn}{samples\PYZus{}generator} \PY{k}{import} \PY{n}{make\PYZus{}blobs}
\PY{n}{sns}\PY{o}{.}\PY{n}{set}\PY{p}{(}\PY{p}{)} \PY{c+c1}{\PYZsh{} for plot styling}
\PY{n}{plt}\PY{o}{.}\PY{n}{style}\PY{o}{.}\PY{n}{use}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{seaborn\PYZhy{}whitegrid}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{fig\PYZus{}width} \PY{o}{=} \PY{l+m+mi}{12}
\PY{n}{fig\PYZus{}height} \PY{o}{=} \PY{l+m+mi}{10}
\PY{c+c1}{\PYZsh{}Samples}
\PY{n}{N\PYZus{}SAMPLES} \PY{o}{=} \PY{l+m+mi}{100000}
\PY{c+c1}{\PYZsh{} Get path of the current dir, then use it to create paths:}
\PY{n}{CURRENT\PYZus{}DIR} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{dirname}\PY{p}{(}\PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{abspath}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{flink\PYZus{}k\PYZhy{}means.ipynb}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{)}
\PY{n}{points\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/input/points\PYZus{}100000.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{centroids\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/input/centroids.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{new\PYZus{}points\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/output/new\PYZus{}points.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{new\PYZus{}centroids\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/output/new\PYZus{}centroids.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{objval\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/output/objfun.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
\hypertarget{initial-dataset}{%
\section{Initial dataset}\label{initial-dataset}}
\hypertarget{points-in-the-initial-dataset}{%
\subsection{Points in the initial
dataset}\label{points-in-the-initial-dataset}}
\begin{itemize}
\tightlist
\item
dataset of 100.000 points, randomly generated
\item
points are already divided into clusters
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}25}]:} \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{points\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{i}\PY{p}{,}\PY{n}{row} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{reader}\PY{p}{)}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{k}{if}\PY{p}{(}\PY{n}{i} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{l+m+mi}{10}\PY{p}{)}\PY{p}{:}
\PY{k}{break}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Total points: }\PY{l+s+si}{\PYZpc{}s}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{format}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{,d}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
X,Y
-6.030655427827744 7.010503797942845
1.44888315638322 5.649841687086858
5.2113349965879365 5.111332892148602
8.169049731285268 -3.0299071227666934
-6.7566857968809675 0.5102043195659359
-6.565675459872967 0.2973336285548338
-5.0923491919544706 7.200424641047177
-9.28377274405066 -4.471524504982716
8.885145705359779 -2.2490604605130797
-10.541767848895473 -5.948723542953223
-5.506572521654158 8.263395622666037
Total points: 100,000
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}26}]:} \PY{n}{x} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}
\PY{n}{y} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Read the dataset from the CVS file}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{points\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{n}{i} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{y}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{i}\PY{o}{=}\PY{n}{i}\PY{o}{+}\PY{l+m+mi}{1}
\PY{c+c1}{\PYZsh{} Plot the read dataset}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{initial-centroids}{%
\subsection{Initial centroids}\label{initial-centroids}}
Initial centroids can be - randomly placed at runtime - recreated if too
close with the ``recompnearest'' input parameter - read from the input
file
\hypertarget{add-header-row-to-centroids}{%
\subparagraph{Add header row to
centroids}\label{add-header-row-to-centroids}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}16}]:} \PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{centroids\PYZus{}path}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r+}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} \PY{k}{as} \PY{n}{f}\PY{p}{:}
\PY{n}{content} \PY{o}{=} \PY{n}{f}\PY{o}{.}\PY{n}{read}\PY{p}{(}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{seek}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{write}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster,X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n}{content}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}27}]:} \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster,X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{centroids} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{centroids} \PY{o}{=} \PY{n}{centroids} \PY{o}{+} \PY{l+m+mi}{1}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Total centroids: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{centroids}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Cluster,X,Y
0 -6.4996390976529295 -4.547264999578333
1 6.534180113636655 -2.488343051409096
2 9.383963677452972 13.631449459607751
3 -9.500499218343863 5.884396961266557
4 8.890352795564372 13.027356262944053
5 9.93075300901236 6.052005456020023
6 13.034049573603387 -1.1265485014145966
7 -11.622709868541028 5.462999295973049
Total centroids: 8
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}28}]:} \PY{n}{x} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{centroids}\PY{p}{)}
\PY{n}{y} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{centroids}\PY{p}{)}
\PY{c+c1}{\PYZsh{}Read the dataset from the CVS file}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{n}{i} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{y}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{i}\PY{o}{=}\PY{n}{i}\PY{o}{+}\PY{l+m+mi}{1}
\PY{c+c1}{\PYZsh{}Plot the read dataset}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{X}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{100}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_10_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{run-flink}{%
\section{Run Flink}\label{run-flink}}
\hypertarget{result-dataset}{%
\section{Result dataset}\label{result-dataset}}
\hypertarget{add-header-row-to-files}{%
\subparagraph{Add header row to files}\label{add-header-row-to-files}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}centroids\PYZus{}path}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r+}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} \PY{k}{as} \PY{n}{f}\PY{p}{:}
\PY{n}{content} \PY{o}{=} \PY{n}{f}\PY{o}{.}\PY{n}{read}\PY{p}{(}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{seek}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{write}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster,X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n}{content}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}points\PYZus{}path}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r+}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} \PY{k}{as} \PY{n}{f}\PY{p}{:}
\PY{n}{content} \PY{o}{=} \PY{n}{f}\PY{o}{.}\PY{n}{read}\PY{p}{(}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{seek}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{f}\PY{o}{.}\PY{n}{write}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster,X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n}{content}\PY{p}{)}
\end{Verbatim}
\hypertarget{plot-new-centroids}{%
\subsection{Plot new centroids}\label{plot-new-centroids}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}29}]:} \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster,X,Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{centroids} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{centroids} \PY{o}{=} \PY{n}{centroids} \PY{o}{+} \PY{l+m+mi}{1}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Total centroids: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{centroids}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Cluster,X,Y
0 -6.018177389534398 -5.970154788636278
1 6.813505758850471 -2.487312645046373
3 -5.415092157412377 6.989688821546183
4 1.1210729942909556 6.365985074051813
5 4.724413665164045 5.2708556118124825
6 8.076399852912724 -2.338271813271596
7 -6.680309422780709 1.8805588389912962
Total centroids: 7
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}30}]:} \PY{n}{x} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{centroids}\PY{p}{)}
\PY{n}{y} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{centroids}\PY{p}{)}
\PY{c+c1}{\PYZsh{}Read the dataset from the CVS file}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{n}{i} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{y}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{c+c1}{\PYZsh{}print(x[i], y[i])}
\PY{n}{i}\PY{o}{=}\PY{n}{i}\PY{o}{+}\PY{l+m+mi}{1}
\PY{c+c1}{\PYZsh{}Plot the read dataset}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{X}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{100}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_17_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{plot-points-new-centroids}{%
\subsection{Plot points + new
centroids}\label{plot-points-new-centroids}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}31}]:} \PY{n}{x} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}
\PY{n}{y} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}
\PY{n}{c} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}
\PY{n}{cx} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{cy} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{cc} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Read the new centroids from the CVS file}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{cx}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{cy}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{cc}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Read the new dataset from the CVS file}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}points\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{n}{i} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{y}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{c}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{c+c1}{\PYZsh{} print(x[i], y[i])}
\PY{n}{i} \PY{o}{=} \PY{n}{i} \PY{o}{+} \PY{l+m+mi}{1}
\PY{n}{minK} \PY{o}{=} \PY{p}{(}\PY{n+nb}{int}\PY{p}{)}\PY{p}{(}\PY{n}{c}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n}{maxK} \PY{o}{=} \PY{p}{(}\PY{n+nb}{int}\PY{p}{)}\PY{p}{(}\PY{n}{c}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{n}{minK}\PY{p}{,} \PY{n}{maxK}\PY{p}{)}
\PY{n}{k} \PY{o}{=} \PY{p}{(}\PY{n+nb}{int}\PY{p}{)}\PY{p}{(}\PY{n}{maxK} \PY{o}{\PYZhy{}} \PY{n}{minK} \PY{o}{+} \PY{l+m+mi}{1}\PY{p}{)}
\PY{c+c1}{\PYZsh{} plot the points for each cluster with a different color}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{minK}\PY{p}{,} \PY{n}{maxK}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{:}
\PY{n}{x2} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{y2} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{N\PYZus{}SAMPLES}\PY{p}{)}\PY{p}{:}
\PY{k}{if} \PY{n}{c}\PY{p}{[}\PY{n}{j}\PY{p}{]} \PY{o}{==} \PY{n}{i}\PY{p}{:}
\PY{n}{x2}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{j}\PY{p}{]}\PY{p}{)}
\PY{n}{y2}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{y}\PY{p}{[}\PY{n}{j}\PY{p}{]}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Plot the read dataset}
\PY{n}{color1} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{random}\PY{o}{.}\PY{n}{rand}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{x2}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{y2}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{c}\PY{o}{=}\PY{n}{color1}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{maxK}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{:}
\PY{n}{color2} \PY{o}{=} \PY{n}{numpy}\PY{o}{.}\PY{n}{random}\PY{o}{.}\PY{n}{rand}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{)}
\PY{k}{try}\PY{p}{:}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{cx}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{cy}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{c}\PY{o}{=}\PY{n}{color2}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{X}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{n}{color2}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{100}\PY{p}{)}
\PY{k}{except}\PY{p}{:}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{No: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{i}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{objval\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{objval\PYZus{}file}\PY{p}{:}
\PY{n}{objval} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{objval\PYZus{}file}\PY{o}{.}\PY{n}{readline}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Obj val: }\PY{l+s+si}{\PYZpc{}f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{objval}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
0 7
No: 7
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_19_1.png}
\end{center}
{ \hspace*{\fill} \\}
\begin{Verbatim}[commandchars=\\\{\}]
Obj val: 567526.857239
\end{Verbatim}
\hypertarget{compute-objective-function}{%
\subsection{Compute objective
function}\label{compute-objective-function}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}32}]:} \PY{k+kn}{import} \PY{n+nn}{math}
\PY{c+c1}{\PYZsh{} read the clusters}
\PY{n}{clusters} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}centroids\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{clusters}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{p}{[}\PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{,} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{,} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Clusters: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{len}\PY{p}{(}\PY{n}{clusters}\PY{p}{)}\PY{p}{)}
\PY{n}{points} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}points\PYZus{}path}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{n}{i} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n}{cp} \PY{o}{=} \PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Cluster}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{xp} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{yp} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{points}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{p}{[}\PY{n}{cp}\PY{p}{,} \PY{n}{xp}\PY{p}{,} \PY{n}{yp}\PY{p}{]}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Points: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{ }\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{len}\PY{p}{(}\PY{n}{points}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} compute the distances and the objective function }
\PY{n}{distances} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{for} \PY{n}{point} \PY{o+ow}{in} \PY{n}{points}\PY{p}{:}
\PY{k}{for} \PY{n}{cluster} \PY{o+ow}{in} \PY{n}{clusters}\PY{p}{:}
\PY{k}{if} \PY{p}{(}\PY{n}{cluster}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{==} \PY{n}{point}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{p}{:}
\PY{n}{distance} \PY{o}{=} \PY{n}{math}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{p}{(}\PY{n}{point}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{cluster}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{p}{(}\PY{n}{point}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{cluster}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{o}{+} \PY{p}{(}\PY{n}{point}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{cluster}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{p}{(}\PY{n}{point}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{cluster}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{distance} \PY{o}{=} \PY{n}{math}\PY{o}{.}\PY{n}{pow}\PY{p}{(}\PY{n}{distance}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}
\PY{n}{distances}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{distance}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Distances: }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s2}{ }\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{len}\PY{p}{(}\PY{n}{distances}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print} \PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Obj function: }\PY{l+s+si}{\PYZpc{}f}\PY{l+s+s2}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{sum}\PY{p}{(}\PY{n}{distances}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Clusters: 7
Points: 100000
Distances: 100000
Obj function: 567526.857239
\end{Verbatim}
\hypertarget{create-new-dataset}{%
\section{Create new dataset}\label{create-new-dataset}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{NEW\PYZus{}SAMPLES}\PY{o}{=}\PY{l+m+mi}{100000}
\PY{n}{NEW\PYZus{}CENTERS}\PY{o}{=}\PY{l+m+mi}{8}
\PY{c+c1}{\PYZsh{}X, y\PYZus{}true = make\PYZus{}blobs(n\PYZus{}samples=N\PYZus{}SAMPLES, centers=4, cluster\PYZus{}std=0.60, random\PYZus{}state=3320)}
\PY{n}{X}\PY{p}{,} \PY{n}{y\PYZus{}true} \PY{o}{=} \PY{n}{make\PYZus{}blobs}\PY{p}{(}\PY{n}{n\PYZus{}samples}\PY{o}{=}\PY{n}{NEW\PYZus{}SAMPLES}\PY{p}{,} \PY{n}{centers}\PY{o}{=}\PY{n}{NEW\PYZus{}CENTERS}\PY{p}{,} \PY{n}{cluster\PYZus{}std}\PY{o}{=}\PY{l+m+mf}{0.60}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{X}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{n}{X}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{n}{s}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_23_0.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{save-dataset-to-file}{%
\subsection{Save dataset to file}\label{save-dataset-to-file}}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{new\PYZus{}points\PYZus{}path} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{files/input/points\PYZus{}}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{NEW\PYZus{}SAMPLES}\PY{p}{)} \PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{new\PYZus{}points\PYZus{}path}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{fieldnames} \PY{o}{=} \PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{writer} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictWriter}\PY{p}{(}\PY{n}{csvfile}\PY{p}{,} \PY{n}{fieldnames}\PY{o}{=}\PY{n}{fieldnames}\PY{p}{)}
\PY{n}{writer}\PY{o}{.}\PY{n}{writeheader}\PY{p}{(}\PY{p}{)}
\PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{NEW\PYZus{}SAMPLES}\PY{p}{)}\PY{p}{:}
\PY{n}{writer}\PY{o}{.}\PY{n}{writerow}\PY{p}{(}\PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{n}{X}\PY{p}{[}\PY{n}{x}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{n}{X}\PY{p}{[}\PY{n}{x}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{\PYZcb{}}\PY{p}{)}
\end{Verbatim}
\begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}
\hypertarget{results}{%
\section{Results}\label{results}}
\hypertarget{objective-function-value}{%
\subsubsection{Objective function
value}\label{objective-function-value}}
\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
Relation between number of centroids and obj function value
\item
Relation between initial distance of centroids and obj function value
\item
Relation between number of iterations and objective function value
\end{enumerate}
\hypertarget{execution-time}{%
\subsubsection{Execution time}\label{execution-time}}
\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\setcounter{enumi}{3}
\tightlist
\item
Relation between number of centroids and execution time
\item
Relation between number of points and the execution time and
parallelism
\end{enumerate}
\hypertarget{relation-between-number-of-centroids-and-obj-function-value-script-1}{%
\subsection{1. Relation between number of centroids and obj function
value (script
1)}\label{relation-between-number-of-centroids-and-obj-function-value-script-1}}
We want to analyze the relation between the number of centroids we use
and the computed objective function value - \textbf{Add one centroid at
a time, randomly generated, {[}1, 20{]} ➡ -numcentroids 1..20} - The
script is executed 5 times for every centroid and the average value is
taken - Fixed input dataset with 8 centers and 100.000 points - 10
iterations ➡ -iterations 10 - No custom aggregator convergence ➡
-custconvergence false - Parallelization set to 4 ➡ -p 4 - Recomputing
of nearest centroid disable ➡ -recompnearest 0
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}98}]:} \PY{n}{obj\PYZus{}mean\PYZus{}vals} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{mink} \PY{o}{=} \PY{l+m+mi}{1}
\PY{n}{maxk} \PY{o}{=} \PY{l+m+mi}{21}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{mink}\PY{p}{,} \PY{n}{maxk}\PY{p}{)}\PY{p}{:}
\PY{n}{fixed\PYZus{}path\PYZus{}objfun} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{script\PYZus{}results/script\PYZus{}1/results\PYZus{}objfun\PYZus{}}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{i}\PY{p}{)} \PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{objval\PYZus{}iter} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{fixed\PYZus{}path\PYZus{}objfun}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n+nb}{iter} \PY{o}{=} \PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{iter}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{objval}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval\PYZus{}iter}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{objval}\PY{p}{)}
\PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{numpy}\PY{o}{.}\PY{n}{average}\PY{p}{(}\PY{n}{objval\PYZus{}iter}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{k+kn}{from} \PY{n+nn}{tabulate} \PY{k}{import} \PY{n}{tabulate}
\PY{n+nb}{print} \PY{p}{(}\PY{n}{tabulate}\PY{p}{(}\PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{,} \PY{n}{headers}\PY{o}{=}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Number of centroids}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj Function Mean Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{x\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{n}{y\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x\PYZus{}val}\PY{p}{,}\PY{n}{y\PYZus{}val}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{suptitle}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Number of centroids \PYZhy{} Obj function mean value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZsh{} of centroids}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Number of centroids Obj Function Mean Value
--------------------- -------------------------
1 5.90974e+06
2 3.30358e+06
3 1.99299e+06
4 1.32618e+06
5 956840
6 729461
7 470450
8 247065
9 332966
10 343733
11 187838
12 161924
13 168307
14 132847
15 135287
16 104812
17 111988
18 105427
19 116363
20 98575.2
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_29_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{the-value-of-the-objective-function-will-decrease-increasing-the-number-of-centroids-until-a-fixed-point-is-reached}{%
\paragraph{The value of the objective function will decrease, increasing
the number of centroids until a fixed point is
reached}\label{the-value-of-the-objective-function-will-decrease-increasing-the-number-of-centroids-until-a-fixed-point-is-reached}}
As we can see the objective function value decreases as the number of
centroid increases until a fixed point is reached and the objective
function value will remain constant even if we add more centroids.
\hypertarget{relation-between-initial-distance-of-centroids-and-obj-function-value-script-2}{%
\subsection{2. Relation between initial distance of centroids and obj
function value (script
2)}\label{relation-between-initial-distance-of-centroids-and-obj-function-value-script-2}}
\begin{itemize}
\tightlist
\item
\textbf{Increasing recomputing of nearest centroid ➡ -recompnearest
{[}0, 10, 20, \ldots{}, 100{]}}
\item
The script is executed 5 times for every recompnearest and the average
value is taken
\item
Fixed input dataset with 8 centers and 100.000 points
\item
8 randomly centroids
\item
Max iterations ➡ -iterations 1
\item
No custom aggregator convergence ➡ -custconvergence false
\item
Parallelization set to 4 ➡ -p 1
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}99}]:} \PY{n}{recomp} \PY{o}{=} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{20}\PY{p}{,}\PY{l+m+mi}{30}\PY{p}{,}\PY{l+m+mi}{40}\PY{p}{,}\PY{l+m+mi}{50}\PY{p}{,}\PY{l+m+mi}{60}\PY{p}{,}\PY{l+m+mi}{70}\PY{p}{,}\PY{l+m+mi}{80}\PY{p}{,}\PY{l+m+mi}{90}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{]}
\PY{n}{obj\PYZus{}mean\PYZus{}vals} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{mink} \PY{o}{=} \PY{l+m+mi}{1}
\PY{n}{maxk} \PY{o}{=} \PY{n+nb}{len}\PY{p}{(}\PY{n}{recomp}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{1}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{mink}\PY{p}{,} \PY{n}{maxk}\PY{p}{)}\PY{p}{:}
\PY{n}{fixed\PYZus{}path\PYZus{}objfun} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{script\PYZus{}results/script\PYZus{}2/results\PYZus{}objfun\PYZus{}}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{i}\PY{p}{)} \PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{objval\PYZus{}iter} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{fixed\PYZus{}path\PYZus{}objfun}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n+nb}{iter} \PY{o}{=} \PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{iter}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{objval}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval\PYZus{}iter}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{objval}\PY{p}{)}
\PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{numpy}\PY{o}{.}\PY{n}{average}\PY{p}{(}\PY{n}{objval\PYZus{}iter}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{n}{x\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{n}{y\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{k+kn}{from} \PY{n+nn}{tabulate} \PY{k}{import} \PY{n}{tabulate}
\PY{n+nb}{print} \PY{p}{(}\PY{n}{tabulate}\PY{p}{(}\PY{p}{\PYZob{}}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Recomp}\PY{l+s+s2}{\PYZdq{}}\PY{p}{:} \PY{n}{recomp}\PY{p}{,}
\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Obj}\PY{l+s+s2}{\PYZdq{}}\PY{p}{:} \PY{n}{y\PYZus{}val}\PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{headers}\PY{o}{=}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Recomp nearest}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj Function Mean Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xticks}\PY{p}{(}\PY{n}{x\PYZus{}val}\PY{p}{,} \PY{n}{recomp}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x\PYZus{}val}\PY{p}{,}\PY{n}{y\PYZus{}val}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{suptitle}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Recompute Nearest \PYZhy{} Obj Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZsh{} recompute nearest}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj fun value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Recomp nearest Obj Function Mean Value
---------------- -------------------------
0 659533
10 611001
20 618168
30 819744
40 547630
50 660676
60 666810
70 553158
80 568986
90 520001
100 649310
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_32_1.png}
\end{center}
{ \hspace*{\fill} \\}
As we can see the objective function values does not decrease as the
number of recomputation increases, due to the nature of the
recomputation implemented. Indeed, the recomputation of the nearest is
done regenerating one point of the nearest couple of points. This method
even if tries to move points one far from another one it is not
deterministic because new centroids are randomly generated and so can
happen that new centroids are close even if they are recomputed a large
number of times
\hypertarget{relation-between-number-of-iterations-and-objective-function-value-script-3}{%
\subsection{3. Relation between number of iterations and objective
function value (script
3)}\label{relation-between-number-of-iterations-and-objective-function-value-script-3}}
\begin{itemize}
\tightlist
\item
\textbf{Execute the script with an increasing number of iterations ➡
-iterations {[}1, 2, 3, \ldots{}, 15{]}}
\item
The script is executed 5 times for every iteration and the average
value is taken
\item
Fixed input dataset with 8 centers and 100.000 points
\item
8 static centroids from file
\item
No custom aggregator convergence ➡ -custconvergence false
\item
Parallelization set to max ➡ -p 1
\item
Recomputing of nearest centroid disable ➡ -recompnearest 0
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}100}]:} \PY{n}{iterations}\PY{o}{=}\PY{n+nb}{range}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{16}\PY{p}{)}
\PY{n}{obj\PYZus{}mean\PYZus{}vals} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{n}{mink} \PY{o}{=} \PY{l+m+mi}{1}
\PY{n}{maxk} \PY{o}{=} \PY{n+nb}{len}\PY{p}{(}\PY{n}{iterations}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{1}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{mink}\PY{p}{,} \PY{n}{maxk}\PY{p}{)}\PY{p}{:}
\PY{n}{fixed\PYZus{}path\PYZus{}objfun} \PY{o}{=} \PY{n}{os}\PY{o}{.}\PY{n}{path}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{CURRENT\PYZus{}DIR}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{script\PYZus{}results/script\PYZus{}3/results\PYZus{}objfun\PYZus{}}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{i}\PY{p}{)} \PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{objval\PYZus{}iter} \PY{o}{=} \PY{n+nb}{list}\PY{p}{(}\PY{p}{)}
\PY{k}{with} \PY{n+nb}{open}\PY{p}{(}\PY{n}{fixed\PYZus{}path\PYZus{}objfun}\PY{p}{)} \PY{k}{as} \PY{n}{csvfile}\PY{p}{:}
\PY{n}{reader} \PY{o}{=} \PY{n}{csv}\PY{o}{.}\PY{n}{DictReader}\PY{p}{(}\PY{n}{csvfile}\PY{p}{)}
\PY{k}{for} \PY{n}{row} \PY{o+ow}{in} \PY{n}{reader}\PY{p}{:}
\PY{n+nb}{iter} \PY{o}{=} \PY{n+nb}{int}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{iter}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval} \PY{o}{=} \PY{n+nb}{float}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{objval}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{objval\PYZus{}iter}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{objval}\PY{p}{)}
\PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{numpy}\PY{o}{.}\PY{n}{average}\PY{p}{(}\PY{n}{objval\PYZus{}iter}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{n}{x\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{n}{y\PYZus{}val} \PY{o}{=} \PY{p}{[}\PY{n}{x}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{k}{for} \PY{n}{x} \PY{o+ow}{in} \PY{n}{obj\PYZus{}mean\PYZus{}vals}\PY{p}{]}
\PY{k+kn}{from} \PY{n+nn}{tabulate} \PY{k}{import} \PY{n}{tabulate}
\PY{n+nb}{print} \PY{p}{(}\PY{n}{tabulate}\PY{p}{(}\PY{p}{\PYZob{}}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Iterations}\PY{l+s+s2}{\PYZdq{}}\PY{p}{:} \PY{n}{iterations}\PY{p}{,}
\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Obj}\PY{l+s+s2}{\PYZdq{}}\PY{p}{:} \PY{n}{y\PYZus{}val}\PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{headers}\PY{o}{=}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Iterations}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj Function Mean Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{n}{fig\PYZus{}width}\PY{p}{,} \PY{n}{fig\PYZus{}height}\PY{p}{)}\PY{p}{,} \PY{n}{dpi}\PY{o}{=} \PY{l+m+mi}{80}\PY{p}{,} \PY{n}{facecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xticks}\PY{p}{(}\PY{n}{x\PYZus{}val}\PY{p}{,} \PY{n}{iterations}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x\PYZus{}val}\PY{p}{,}\PY{n}{y\PYZus{}val}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{suptitle}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Number of iterations \PYZhy{} Obj Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZsh{} number of iterations}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Obj fun value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Iterations Obj Function Mean Value
------------ -------------------------
1 541541
2 308055
3 288017
4 277546
5 270415
6 266614
7 265335
8 265055
9 265002
10 264993
11 264992
12 264992
13 264992
14 264992
15 264992