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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>demo_emgmm.m</title><link rel="stylesheet" type="text/css" href="../../m-syntax.css"></head><body><code><span class=defun_kw>function</span>&nbsp;<span class=defun_name>demo_emgmm</span>(<span class=defun_in>action,hfigure,varargin</span>)<br><span class=h1>%&nbsp;DEMO_EMGMM&nbsp;Demo&nbsp;on&nbsp;Expectation-Maximization&nbsp;(EM)&nbsp;algorithm.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Synopsis:</span></span><br><span class=help>%&nbsp;&nbsp;demo_emgmm</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Description:</span></span><br><span class=help>%&nbsp;&nbsp;This&nbsp;demo&nbsp;shows&nbsp;the&nbsp;Expectation-Maximization&nbsp;(EM)&nbsp;algorithm</span><br><span class=help>%&nbsp;&nbsp;[Schles68][DLR77]&nbsp;for&nbsp;Gaussians&nbsp;mixture&nbsp;model&nbsp;(GMM).&nbsp;The&nbsp;EM&nbsp;</span><br><span class=help>%&nbsp;&nbsp;fits&nbsp;the&nbsp;GMM&nbsp;to&nbsp;i.i.d.&nbsp;sample&nbsp;data&nbsp;(in&nbsp;this&nbsp;case&nbsp;only&nbsp;2D)&nbsp;</span><br><span class=help>%&nbsp;&nbsp;such&nbsp;that&nbsp;the&nbsp;likelihood&nbsp;is&nbsp;maximized.&nbsp;</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;The&nbsp;found&nbsp;model&nbsp;is&nbsp;described&nbsp;by&nbsp;ellipsoids&nbsp;(shape&nbsp;of&nbsp;</span><br><span class=help>%&nbsp;&nbsp;covariances)&nbsp;and&nbsp;a&nbsp;crosses&nbsp;(mean&nbsp;value&nbsp;vectors).&nbsp;The&nbsp;value</span><br><span class=help>%&nbsp;&nbsp;of&nbsp;the&nbsp;optimized&nbsp;log-likelihood&nbsp;function&nbsp;for&nbsp;the&nbsp;current&nbsp;estimate&nbsp;</span><br><span class=help>%&nbsp;&nbsp;is&nbsp;displayed&nbsp;in&nbsp;the&nbsp;bottom&nbsp;part.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Control:</span></span><br><span class=help>%&nbsp;&nbsp;Covariance&nbsp;&nbsp;-&nbsp;Determines&nbsp;type&nbsp;of&nbsp;the&nbsp;covariance&nbsp;matrix:</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Diagonal&nbsp;(independent&nbsp;features),</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Full&nbsp;(correlated&nbsp;features).</span><br><span class=help>%&nbsp;&nbsp;Components&nbsp;&nbsp;-&nbsp;Number&nbsp;of&nbsp;components&nbsp;(Gaussians)&nbsp;in&nbsp;the&nbsp;mixture.</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><br><span class=help>%&nbsp;&nbsp;Iterations&nbsp;&nbsp;-&nbsp;Number&nbsp;of&nbsp;iterations&nbsp;in&nbsp;one&nbsp;step.</span><br><span class=help>%&nbsp;&nbsp;Random&nbsp;init&nbsp;-&nbsp;the&nbsp;initial&nbsp;model&nbsp;is&nbsp;randomly&nbsp;generated&nbsp;and/or&nbsp;</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;first&nbsp;n&nbsp;training&nbsp;samples&nbsp;are&nbsp;taken&nbsp;as&nbsp;the</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;mean&nbsp;vectors.</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;FIG2EPS&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Export&nbsp;screen&nbsp;to&nbsp;the&nbsp;PostScript&nbsp;file.</span><br><span class=help>%&nbsp;&nbsp;Save&nbsp;model&nbsp;&nbsp;-&nbsp;Save&nbsp;current&nbsp;model&nbsp;to&nbsp;file.</span><br><span class=help>%&nbsp;&nbsp;Load&nbsp;data&nbsp;&nbsp;&nbsp;-&nbsp;Load&nbsp;input&nbsp;point&nbsp;sets&nbsp;from&nbsp;file.</span><br><span class=help>%&nbsp;&nbsp;Create&nbsp;data&nbsp;-&nbsp;Invoke&nbsp;program&nbsp;for&nbsp;creating&nbsp;point&nbsp;sets.</span><br><span class=help>%&nbsp;&nbsp;Reset&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Set&nbsp;the&nbsp;tested&nbsp;algorithm&nbsp;to&nbsp;the&nbsp;initial&nbsp;state.</span><br><span class=help>%&nbsp;&nbsp;Play&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Run&nbsp;the&nbsp;tested&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Stop&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Stop&nbsp;the&nbsp;running&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Step&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Perform&nbsp;only&nbsp;one&nbsp;step.</span><br><span class=help>%&nbsp;&nbsp;Info&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Info&nbsp;box.</span><br><span class=help>%&nbsp;&nbsp;Close&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Close&nbsp;the&nbsp;program.</span><br><span class=help>%</span><br><span class=help>%&nbsp;See&nbsp;also&nbsp;EMGMM.</span><br><span class=help>%</span><br><hr><span class=help1>%&nbsp;<span class=help1_field>About:</span>&nbsp;Statistical&nbsp;Pattern&nbsp;Recognition&nbsp;Toolbox</span><br><span class=help1>%&nbsp;(C)&nbsp;1999-2003,&nbsp;Written&nbsp;by&nbsp;Vojtech&nbsp;Franc&nbsp;and&nbsp;Vaclav&nbsp;Hlavac</span><br><span class=help1>%&nbsp;&lt;a&nbsp;href="http://www.cvut.cz"&gt;Czech&nbsp;Technical&nbsp;University&nbsp;Prague&lt;/a&gt;</span><br><span class=help1>%&nbsp;&lt;a&nbsp;href="http://www.feld.cvut.cz"&gt;Faculty&nbsp;of&nbsp;Electrical&nbsp;Engineering&lt;/a&gt;</span><br><span class=help1>%&nbsp;&lt;a&nbsp;href="http://cmp.felk.cvut.cz"&gt;Center&nbsp;for&nbsp;Machine&nbsp;Perception&lt;/a&gt;</span><br><br><span class=help1>%&nbsp;<span class=help1_field>Modifications:</span></span><br><span class=help1>%&nbsp;19-sep-2003,&nbsp;VF</span><br><span class=help1>%&nbsp;11-june-2001,&nbsp;V.Franc,&nbsp;comments&nbsp;added.</span><br><span class=help1>%&nbsp;27.02.00&nbsp;V.&nbsp;Franc</span><br><span class=help1>%&nbsp;&nbsp;5.&nbsp;4.00&nbsp;V.&nbsp;Franc</span><br><span class=help1>%&nbsp;23.06.00&nbsp;V.&nbsp;Hlavac&nbsp;Comments&nbsp;polished.&nbsp;Message&nbsp;when&nbsp;no&nbsp;data&nbsp;loaded.</span><br><span class=help1>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Export&nbsp;of&nbsp;the&nbsp;solution&nbsp;to&nbsp;global&nbsp;variables.</span><br><span class=help1>%&nbsp;27-mar-2001,&nbsp;V.Franc,&nbsp;Graph&nbsp;og&nbsp;log-likelihood&nbsp;function&nbsp;added</span><br><br><br><hr><span class=comment>%&nbsp;Used&nbsp;functions:&nbsp;PPOINTS,&nbsp;PNMIX</span><br><br><span class=comment>%&nbsp;==&nbsp;Global&nbsp;variables,&nbsp;used&nbsp;to&nbsp;export&nbsp;results&nbsp;from&nbsp;demo_emgmm&nbsp;========</span><br><br><span class=type>global</span>&nbsp;UNSU_MI&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;K&nbsp;vectors&nbsp;with&nbsp;mean&nbsp;values</span><br><span class=type>global</span>&nbsp;UNSU_SIGMA&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;K&nbsp;covariance&nbsp;matrices</span><br><span class=type>global</span>&nbsp;UNSU_PK&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;K&nbsp;apriori&nbsp;probabilities&nbsp;for&nbsp;each&nbsp;distributions.</span><br><span class=comment>%global&nbsp;UNSU_eI&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%&nbsp;Used&nbsp;only&nbsp;by&nbsp;the&nbsp;next&nbsp;iteration,&nbsp;not&nbsp;globalised</span><br><span class=type>global</span>&nbsp;UNSU_solution&nbsp;<span class=comment>%&nbsp;1&nbsp;if&nbsp;alg.&nbsp;finished&nbsp;in&nbsp;stationary&nbsp;point,&nbsp;0&nbsp;otherwise</span><br><span class=type>global</span>&nbsp;UNSU_t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Number&nbsp;of&nbsp;iterations&nbsp;the&nbsp;algorithm&nbsp;performed</span><br><br><span class=comment>%&nbsp;==&nbsp;Constants&nbsp;=====================================================</span><br><br>AXIST_ADD=10;<br>AXISY_ADD=5;<br><br>BORDER=0.25;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;space&nbsp;betwean&nbsp;window&nbsp;outer&nbsp;and&nbsp;the&nbsp;points
</span><br>CENTERSIZE=10;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;size&nbsp;of&nbsp;center&nbsp;point
</span><br>LINE_WIDTH=1;
<br>AXIST_ADD=10;
<br>DATA_IDENT=<span class=quotes>'Finite&nbsp;sets,&nbsp;enumeration'</span>;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;file&nbsp;identifier
</span><br>randinit=1;
<br>
<br><span class=keyword>if</span>&nbsp;<span class=stack>nargin</span>&nbsp;&lt;&nbsp;1,
<br>&nbsp;&nbsp;&nbsp;action&nbsp;=&nbsp;<span class=quotes>'initialize'</span>;
<br><span class=keyword>end</span>
<br>
<br><span class=comment>%&nbsp;What&nbsp;action&nbsp;is&nbsp;required&nbsp;?
</span><br><span class=keyword>switch</span>&nbsp;lower(action)
<br>
<br><span class=label>case</span>&nbsp;<span class=quotes>'initialize'</span>
<br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;==&nbsp;Initialize&nbsp;user&nbsp;interface&nbsp;control&nbsp;and&nbsp;figure&nbsp;window&nbsp;================
</span><br>
<br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;==&nbsp;Figure</span><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;=============================================================
</span><br>&nbsp;&nbsp;&nbsp;left=0.2;<br>&nbsp;&nbsp;&nbsp;width=0.6;<br>&nbsp;&nbsp;&nbsp;bottom=0.1;<br>&nbsp;&nbsp;&nbsp;height=0.8;<br>&nbsp;&nbsp;&nbsp;hfigure=<span class=graph>figure</span>(<span class=quotes>'Name'</span>,<span class=quotes>'EM&nbsp;algorithm'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Visible'</span>,<span class=quotes>'off'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'NumberTitle'</span>,<span class=quotes>'off'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Units'</span>,<span class=quotes>'normalized'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[left&nbsp;bottom&nbsp;width&nbsp;height],...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'tag'</span>,<span class=quotes>'demo_emgmm'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'doublebuffer'</span>,<span class=quotes>'on'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'backingstore'</span>,<span class=quotes>'off'</span>);<br><br>&nbsp;&nbsp;&nbsp;<br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;==&nbsp;Axes&nbsp;===============================================================</span><br>&nbsp;&nbsp;&nbsp;left=0.1;<br>&nbsp;&nbsp;&nbsp;width=0.65;<br>&nbsp;&nbsp;&nbsp;bottom=0.45;<br>&nbsp;&nbsp;&nbsp;height=0.5;<br>&nbsp;&nbsp;&nbsp;haxes1=<span class=graph>axes</span>(...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Units'</span>,<span class=quotes>'normalized'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'NextPlot'</span>,<span class=quotes>'add'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'UserData'</span>,[],...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[left&nbsp;bottom&nbsp;width&nbsp;height]);<br>&nbsp;&nbsp;&nbsp;xlabel(<span class=quotes>'feature&nbsp;x\_1'</span>);<br>&nbsp;&nbsp;&nbsp;ylabel(<span class=quotes>'feature&nbsp;x\_2'</span>);<br><br>&nbsp;&nbsp;&nbsp;htitle1=title(<span class=quotes>'No&nbsp;data&nbsp;loaded'</span>,...
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'VerticalAlignment'</span>,<span class=quotes>'bottom'</span>,...
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Parent'</span>,haxes1,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'HorizontalAlignment'</span>,<span class=quotes>'left'</span>,...
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Units'</span>,<span class=quotes>'normalized'</span>,...
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[0&nbsp;1&nbsp;0]);
<br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;axes&nbsp;log-Likelihood&nbsp;graph</span><br>&nbsp;&nbsp;&nbsp;left=0.1;<br>&nbsp;&nbsp;&nbsp;width=0.65;<br>&nbsp;&nbsp;&nbsp;bottom=0.1;<br>&nbsp;&nbsp;&nbsp;height=0.25;<br>&nbsp;&nbsp;&nbsp;haxes2=<span class=graph>axes</span>(...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Units'</span>,<span class=quotes>'normalized'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'NextPlot'</span>,<span class=quotes>'add'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[left&nbsp;bottom&nbsp;width&nbsp;height]);<br>&nbsp;&nbsp;&nbsp;ylabel(<span class=quotes>'logL(t)'</span>);<br>&nbsp;&nbsp;&nbsp;<br>&nbsp;&nbsp;&nbsp;htitle2=title(<span class=quotes>'Log-likelihood&nbsp;function'</span>,...<br>
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