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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>demo_mmgauss.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_mmgauss</span>(<span class=defun_in>action,hfigure,varargin</span>)<br><span class=h1>%&nbsp;DEMO_MMGAUSS&nbsp;Demo&nbsp;on&nbsp;minimax&nbsp;estimation&nbsp;for&nbsp;Gaussian.</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_mmgauss</span><br><span class=help>%&nbsp;</span><br><span class=help>%&nbsp;<span class=help_field>Description:</span></span><br><span class=help>%&nbsp;&nbsp;demo_mmgauss&nbsp;demonstrates&nbsp;the&nbsp;minimax&nbsp;estimation&nbsp;algorithm&nbsp;</span><br><span class=help>%&nbsp;&nbsp;[SH10]&nbsp;for&nbsp;bivariate&nbsp;Gaussian&nbsp;distribution.&nbsp;The&nbsp;training&nbsp;data&nbsp;</span><br><span class=help>%&nbsp;&nbsp;is&nbsp;supposed&nbsp;to&nbsp;contain&nbsp;samples&nbsp;which&nbsp;well&nbsp;describing&nbsp;the&nbsp;</span><br><span class=help>%&nbsp;&nbsp;probability&nbsp;distribution&nbsp;function&nbsp;(pdf),&nbsp;i.e.,&nbsp;which&nbsp;have&nbsp;</span><br><span class=help>%&nbsp;&nbsp;high&nbsp;value&nbsp;of&nbsp;pdf.&nbsp;The&nbsp;samples&nbsp;do&nbsp;not&nbsp;have&nbsp;to&nbsp;be&nbsp;i.i.d.&nbsp;in&nbsp;</span><br><span class=help>%&nbsp;&nbsp;contrast&nbsp;to&nbsp;the&nbsp;ML&nbsp;estimation.</span><br><span class=help>%&nbsp;&nbsp;</span><br><span class=help>%&nbsp;&nbsp;The&nbsp;estimated&nbsp;model&nbsp;is&nbsp;visualized&nbsp;as&nbsp;an&nbsp;ellipsoid:</span><br><span class=help>%&nbsp;&nbsp;shape&nbsp;is&nbsp;influenced&nbsp;by&nbsp;the&nbsp;covariance&nbsp;matrix&nbsp;and&nbsp;the&nbsp;center</span><br><span class=help>%&nbsp;&nbsp;corresponds&nbsp;to&nbsp;the&nbsp;mean&nbsp;vector.</span><br><span class=help>%&nbsp;&nbsp;The&nbsp;lower&nbsp;(red)&nbsp;and&nbsp;upper&nbsp;(blue)&nbsp;bound&nbsp;on&nbsp;the&nbsp;optimal&nbsp;value&nbsp;</span><br><span class=help>%&nbsp;&nbsp;of&nbsp;the&nbsp;optimized&nbsp;minimax&nbsp;criterion&nbsp;is&nbsp;displayed&nbsp;at&nbsp;the&nbsp;bottom</span><br><span class=help>%&nbsp;&nbsp;part&nbsp;of&nbsp;the&nbsp;window.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Control:</span></span><br><span class=help>%&nbsp;&nbsp;Epsilon&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Stopping&nbsp;condition.&nbsp;The&nbsp;algorithm&nbsp;stops&nbsp;if&nbsp;the&nbsp;</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;difference&nbsp;between&nbsp;lower&nbsp;and&nbsp;the&nbsp;upper&nbsp;bound</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;less&nbsp;then&nbsp;the&nbsp;epsilon.</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;after&nbsp;which&nbsp;the&nbsp;model&nbsp;</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;re-displayed.</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;FIG2EPS&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Exports&nbsp;figure&nbsp;to&nbsp;the&nbsp;PostScript&nbsp;file.</span><br><span class=help>%&nbsp;&nbsp;Load&nbsp;data&nbsp;&nbsp;&nbsp;-&nbsp;Loads&nbsp;input&nbsp;data&nbsp;sample&nbsp;from&nbsp;file.</span><br><span class=help>%&nbsp;&nbsp;Create&nbsp;data&nbsp;-&nbsp;Invokes&nbsp;program&nbsp;for&nbsp;creating&nbsp;data&nbsp;sample.</span><br><span class=help>%&nbsp;&nbsp;Reset&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Resets&nbsp;the&nbsp;demo.</span><br><span class=help>%&nbsp;&nbsp;Play&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Runs&nbsp;the&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Stop&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Stops&nbsp;the&nbsp;running&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Step&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Performs&nbsp;one&nbsp;iteration&nbsp;of&nbsp;the&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Info&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Invokes&nbsp;the&nbsp;info&nbsp;box.</span><br><span class=help>%&nbsp;&nbsp;Close&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;Closes&nbsp;the&nbsp;program.</span><br><span class=help>%</span><br><span class=help>%&nbsp;See&nbsp;also&nbsp;MMGAUSS.</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;2-may-2004,&nbsp;VF</span><br><span class=help1>%&nbsp;19-sep-2003,&nbsp;VF</span><br><span class=help1>%&nbsp;3-mar-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;24.&nbsp;6.00&nbsp;V.&nbsp;Hlavac,&nbsp;comments&nbsp;polished.</span><br><br><hr><span class=comment>%&nbsp;Used&nbsp;functions:&nbsp;PPOINTS,&nbsp;ELLIPS</span><br><br>BORDER=0.25;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;space&nbsp;between&nbsp;window&nbsp;limits&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><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&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>'Minimax&nbsp;learning'</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_mmgauss'</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;<span class=comment>%&nbsp;==&nbsp;Axes&nbsp;===============================================================</span><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;axes&nbsp;with&nbsp;prob.</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=0.28;<br>&nbsp;&nbsp;&nbsp;haprob=<span class=graph>axes</span>(...<br>&nbsp;&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;title(<span class=quotes>'blue&nbsp;-&nbsp;log&nbsp;p(x),&nbsp;red&nbsp;-&nbsp;\Sigma&nbsp;\alpha(x)&nbsp;log&nbsp;p(x)'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Parent'</span>,haprob,...<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>'Units'</span>,<span class=quotes>'normalized'</span>,...<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>'Position'</span>,[0&nbsp;1&nbsp;0]);<br>&nbsp;&nbsp;&nbsp;htxsteps=xlabel(<span class=quotes>'step&nbsp;number'</span>);<br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;points</span><br>&nbsp;&nbsp;&nbsp;height=0.45;<br>&nbsp;&nbsp;&nbsp;bottom=0.5;<br><span class=comment>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'XTick',[],'YTick',[],&nbsp;...</span><br>&nbsp;&nbsp;&nbsp;haset=<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>'feature&nbsp;y'</span>);<br>&nbsp;&nbsp;&nbsp;xlabel(<span class=quotes>'feature&nbsp;x'</span>);<br><br>&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;==&nbsp;Buttons&nbsp;===========================================================</span><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;--&nbsp;Export&nbsp;to&nbsp;EPS&nbsp;---------</span><br>&nbsp;&nbsp;&nbsp;width=0.1;<br>&nbsp;&nbsp;&nbsp;left=0.75-width;<br>&nbsp;&nbsp;&nbsp;bottom=0.95;<br>&nbsp;&nbsp;&nbsp;height=0.04;<br>&nbsp;&nbsp;&nbsp;hbtclose&nbsp;=&nbsp;<span class=graph>uicontrol</span>(...<br>&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>'Callback'</span>,<span class=quotes>'fig2eps(gcf)'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'ListboxTop'</span>,0,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[left&nbsp;bottom&nbsp;width&nbsp;height],&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'String'</span>,<span class=quotes>'FIG2EPS'</span>);<br>&nbsp;&nbsp;&nbsp;<span class=comment>%----------------------------------</span><br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Close&nbsp;button</span><br>&nbsp;&nbsp;&nbsp;left=0.8;<br>&nbsp;&nbsp;&nbsp;bottom=0.05;<br>&nbsp;&nbsp;&nbsp;height=0.05;<br>&nbsp;&nbsp;&nbsp;width=0.15;<br>&nbsp;&nbsp;&nbsp;hbtclose&nbsp;=&nbsp;<span class=graph>uicontrol</span>(...<br>&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>'Callback'</span>,<span class=quotes>'close(gcf)'</span>,...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'ListboxTop'</span>,0,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Position'</span>,[left&nbsp;bottom&nbsp;width&nbsp;height],&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'String'</span>,<span class=quotes>'Close'</span>);<br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Info&nbsp;button:&nbsp;call&nbsp;stanard&nbsp;info&nbsp;box</span><br>
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