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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>demo_anderson.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_out>result&nbsp;</span>=&nbsp;<span class=defun_name>demo_anderson</span>(<span class=defun_in>action,hfigure,varargin</span>)<br><span class=h1>%&nbsp;DEMO_ANDERSON&nbsp;Demo&nbsp;on&nbsp;Generalized&nbsp;Anderson's&nbsp;task.</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_anderson</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;demonstrates&nbsp;the&nbsp;algorithms&nbsp;which&nbsp;solve&nbsp;</span><br><span class=help>%&nbsp;&nbsp;the&nbsp;Generalized&nbsp;Anderson`s&nbsp;Task&nbsp;(GAT)&nbsp;[SH10].&nbsp;The&nbsp;GAT&nbsp;is&nbsp;an&nbsp;</span><br><span class=help>%&nbsp;&nbsp;instance&nbsp;of&nbsp;the&nbsp;non-Bayesian&nbsp;task&nbsp;of&nbsp;decision&nbsp;under&nbsp;</span><br><span class=help>%&nbsp;&nbsp;non-random&nbsp;intervention.&nbsp;</span><br><span class=help>%&nbsp;</span><br><span class=help>%&nbsp;&nbsp;The&nbsp;goal&nbsp;of&nbsp;is&nbsp;to&nbsp;find&nbsp;a&nbsp;binary&nbsp;linear&nbsp;classification</span><br><span class=help>%&nbsp;&nbsp;rule&nbsp;(g(x)=sgn(W'*x+b)&nbsp;(line&nbsp;in&nbsp;2D)&nbsp;with&nbsp;minimal&nbsp;probability&nbsp;of</span><br><span class=help>%&nbsp;&nbsp;misclassification.&nbsp;The&nbsp;conditional&nbsp;probabilities&nbsp;are&nbsp;known&nbsp;to</span><br><span class=help>%&nbsp;&nbsp;be&nbsp;Gaussians&nbsp;their&nbsp;paramaters&nbsp;belong&nbsp;to&nbsp;a&nbsp;given&nbsp;set&nbsp;of&nbsp;</span><br><span class=help>%&nbsp;&nbsp;parameters.&nbsp;The&nbsp;true&nbsp;parameters&nbsp;are&nbsp;not&nbsp;known.&nbsp;The&nbsp;linear&nbsp;rule&nbsp;</span><br><span class=help>%&nbsp;&nbsp;which&nbsp;guarantes&nbsp;the&nbsp;minimimal&nbsp;classification&nbsp;error&nbsp;for&nbsp;the&nbsp;worst</span><br><span class=help>%&nbsp;&nbsp;possible&nbsp;case&nbsp;(the&nbsp;worst&nbsp;configuration&nbsp;of&nbsp;Gaussains)&nbsp;is</span><br><span class=help>%&nbsp;&nbsp;sought&nbsp;for.</span><br><span class=help>%&nbsp;&nbsp;</span><br><span class=help>%&nbsp;&nbsp;The&nbsp;found&nbsp;solution&nbsp;(hyperplane,&nbsp;line&nbsp;in&nbsp;2D)&nbsp;is&nbsp;vizualized&nbsp;</span><br><span class=help>%&nbsp;&nbsp;as&nbsp;well&nbsp;as&nbsp;the&nbsp;input&nbsp;Gaussians&nbsp;which&nbsp;describe&nbsp;input&nbsp;classes.</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;Following&nbsp;algorithms&nbsp;can&nbsp;be&nbsp;tested:</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><br><span class=help>%&nbsp;&nbsp;Eps-solution&nbsp;-&nbsp;Finds&nbsp;epsilon-solution&nbsp;of&nbsp;the&nbsp;GAT&nbsp;in&nbsp;finite&nbsp;number</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of&nbsp;iterations&nbsp;if&nbsp;such&nbsp;solution&nbsp;exist.&nbsp;The&nbsp;epsilon&nbsp;means</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;desired&nbsp;classification&nbsp;error.</span><br><span class=help>%&nbsp;&nbsp;Original&nbsp;&nbsp;-&nbsp;Original&nbsp;Anderson-Bahadur's&nbsp;algorithm&nbsp;defined&nbsp;for&nbsp;</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;two&nbsp;Gaussians&nbsp;only&nbsp;(each&nbsp;class&nbsp;one&nbsp;Gaussian).</span><br><span class=help>%&nbsp;&nbsp;Optimal&nbsp;&nbsp;&nbsp;-&nbsp;Implementation&nbsp;of&nbsp;general&nbsp;algorithm&nbsp;propsed&nbsp;by&nbsp;Schlesinger.</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It&nbsp;finds&nbsp;the&nbsp;optimal&nbsp;solution.</span><br><span class=help>%&nbsp;&nbsp;Gradient&nbsp;&nbsp;-&nbsp;Fast&nbsp;and&nbsp;simple&nbsp;implementation&nbsp;which&nbsp;uses&nbsp;the&nbsp;generalized</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;gradient&nbsp;descent&nbsp;optimization.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Control:</span></span><br><span class=help>%&nbsp;&nbsp;Algorithm&nbsp;&nbsp;-&nbsp;select&nbsp;algorithm&nbsp;for&nbsp;testing.</span><br><span class=help>%&nbsp;&nbsp;Parameter&nbsp;&nbsp;-&nbsp;parameters&nbsp;for&nbsp;the&nbsp;selected&nbsp;algorithm.</span><br><span class=help>%&nbsp;&nbsp;Iterations&nbsp;-&nbsp;number&nbsp;of&nbsp;iterations&nbsp;in&nbsp;one&nbsp;step.</span><br><span class=help>%&nbsp;&nbsp;Animation&nbsp;&nbsp;-&nbsp;enable/dissable&nbsp;animation.</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;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;call&nbsp;interactive&nbsp;program&nbsp;for&nbsp;creating&nbsp;sets&nbsp;of&nbsp;Gaussians.</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;display&nbsp;the&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;</span><br><span class=help>%&nbsp;&nbsp;EANDERS,&nbsp;ANDRORIG,&nbsp;GGRADANDR,&nbsp;GANDERS.</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;17-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;24.&nbsp;6.00&nbsp;V.&nbsp;Hlavac,&nbsp;comments&nbsp;polished.</span><br><br><hr><span class=comment>%&nbsp;constants</span><br>ALGONAMES=[<span class=quotes>'Eps-solution&nbsp;'</span>;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Original&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'</span>;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Gradient&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'</span>;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Optimal&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'</span>];<br>PREC_TITLE=[<span class=quotes>'Max&nbsp;error&nbsp;(0-50)&nbsp;[%]'</span>;...&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;e-Optimal&nbsp;solution</span><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'d(lambda,ni)&nbsp;(0,inf)'</span>;...&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Original&nbsp;Anderson`s&nbsp;solution</span><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'d(&nbsp;min&nbsp;r&nbsp;)&nbsp;(0,inf)&nbsp;&nbsp;'</span>;...&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Gradient&nbsp;method</span><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'d(&nbsp;min&nbsp;r&nbsp;)&nbsp;(0,inf)&nbsp;&nbsp;'</span>];&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;General&nbsp;solution&nbsp;</span><br>DEF_PRECISION=[10,1e-3,1e-3,1e-3];&nbsp;&nbsp;<span class=comment>%&nbsp;default&nbsp;values&nbsp;of&nbsp;the&nbsp;precision&nbsp;of&nbsp;algo.&nbsp;1,2,...</span><br>BORDER=0.5;<br>DATA_IDENT=<span class=quotes>'Infinite&nbsp;sets,&nbsp;Normal&nbsp;distributions'</span>;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;M-file&nbsp;identifier</span><br>PLOT_FCE=<span class=quotes>'pandr2d'</span>;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;outlined&nbsp;ellipsoids</span><br><span class=comment>%PLOT_FCE='pandr2df';&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%&nbsp;outlined&nbsp;ellipsoids</span><br><br><span class=comment>%&nbsp;if&nbsp;number&nbsp;of&nbsp;arguments&nbsp;is&nbsp;less&nbsp;then&nbsp;1,&nbsp;that&nbsp;means&nbsp;first&nbsp;call&nbsp;of&nbsp;this&nbsp;function.&nbsp;Every</span><br><span class=comment>%&nbsp;other&nbsp;calls&nbsp;set&nbsp;up&nbsp;at&nbsp;least&nbsp;argument&nbsp;action</span><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=0.1;<br>&nbsp;&nbsp;&nbsp;width=0.8;<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>'Anderson`s&nbsp;task'</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>'Units'</span>,<span class=quotes>'normalized'</span>,&nbsp;...<br>&nbsp;&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>'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_Anderson'</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>'RendererMode'</span>,<span class=quotes>'manual'</span>);<br><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><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;axes&nbsp;for&nbsp;showing&nbsp;sets</span><br>&nbsp;&nbsp;&nbsp;bottom=0.35;<br>&nbsp;&nbsp;&nbsp;height=0.60;<br>&nbsp;&nbsp;&nbsp;haxes1=<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>'Box'</span>,<span class=quotes>'on'</span>,&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'DrawMode'</span>,<span class=quotes>'fast'</span>,...<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>'Layer'</span>,<span class=quotes>'top'</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'</span>);<br>&nbsp;&nbsp;&nbsp;ylabel(<span class=quotes>'feature&nbsp;y'</span>);<br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;==&nbsp;Comment&nbsp;window&nbsp;=====================================================</span><br><br>&nbsp;&nbsp;&nbsp;<span class=comment>%&nbsp;Comment&nbsp;Window&nbsp;frame</span><br>&nbsp;&nbsp;&nbsp;bottom=0.05;<br>&nbsp;&nbsp;&nbsp;height=0.2;<br>&nbsp;&nbsp;&nbsp;<span class=graph>uicontrol</span>(&nbsp;...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=quotes>'Style'</span>,<span class=quotes>'frame'</span>,&nbsp;...<br>&nbsp;&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;&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>'BackgroundColor'</span>,[0.5&nbsp;0.5&nbsp;0.5]);<br><br>
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