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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>quadclass.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>[y,dfce]</span>=<span class=defun_name>quadclass</span>(<span class=defun_in>&nbsp;X,&nbsp;model</span>)<br><span class=h1>%&nbsp;QUADCLASS&nbsp;Quadratic&nbsp;classifier.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Synopsis:</span></span><br><span class=help>%&nbsp;&nbsp;[y,dfce]&nbsp;=&nbsp;quadclass(X,model)</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;function&nbsp;classifies&nbsp;input&nbsp;data&nbsp;X&nbsp;using&nbsp;quadratic</span><br><span class=help>%&nbsp;&nbsp;discriminant&nbsp;function:</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;y(i)&nbsp;=&nbsp;argmax&nbsp;X(:,i)'*A(:,:,y)*X(:,i)&nbsp;+&nbsp;X(:,i)'*B(:,y)&nbsp;+&nbsp;C(y)</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;where&nbsp;parameters&nbsp;A&nbsp;[dim&nbsp;x&nbsp;dim&nbsp;x&nbsp;nfun],&nbsp;B&nbsp;[dim&nbsp;x&nbsp;nfun]</span><br><span class=help>%&nbsp;&nbsp;and&nbsp;model&nbsp;C&nbsp;[1&nbsp;x&nbsp;nfun]&nbsp;are&nbsp;given&nbsp;in&nbsp;model&nbsp;and&nbsp;nfun&nbsp;is</span><br><span class=help>%&nbsp;&nbsp;number&nbsp;of&nbsp;discriminant&nbsp;functions.</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;In&nbsp;the&nbsp;binary&nbsp;case&nbsp;(nfun=1)&nbsp;the&nbsp;classification&nbsp;rule&nbsp;is&nbsp;following</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;y(i)&nbsp;=&nbsp;1&nbsp;if&nbsp;X(:,i)'*A*X(:,i)&nbsp;+&nbsp;X(:,i)'*B&nbsp;+&nbsp;C&nbsp;&gt;=&nbsp;0</span><br><span class=help>%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;if&nbsp;X(:,i)'*A*X(:,i)&nbsp;+&nbsp;X(:,i)'*B&nbsp;+&nbsp;C&nbsp;&lt;&nbsp;0</span><br><span class=help>%&nbsp;&nbsp;</span><br><span class=help>%&nbsp;&nbsp;where&nbsp;A&nbsp;[dim&nbsp;x&nbsp;dim],&nbsp;B&nbsp;[dim&nbsp;x&nbsp;1]&nbsp;and&nbsp;C&nbsp;[1x1]&nbsp;are&nbsp;parameters</span><br><span class=help>%&nbsp;&nbsp;given&nbsp;in&nbsp;model.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Input:</span></span><br><span class=help>%&nbsp;&nbsp;X&nbsp;[dim&nbsp;x&nbsp;num_data]&nbsp;Data&nbsp;to&nbsp;be&nbsp;classified.</span><br><span class=help>%</span><br><span class=help>%&nbsp;&nbsp;model&nbsp;[struct]&nbsp;Describes&nbsp;quadratic&nbsp;classifier:</span><br><span class=help>%&nbsp;&nbsp;&nbsp;.A&nbsp;[dim&nbsp;x&nbsp;dim&nbsp;x&nbsp;nfun]&nbsp;Parameter&nbsp;of&nbsp;quadratic&nbsp;term.</span><br><span class=help>%&nbsp;&nbsp;&nbsp;.B&nbsp;[dim&nbsp;x&nbsp;nfun]&nbsp;Parameter&nbsp;of&nbsp;linear&nbsp;term.</span><br><span class=help>%&nbsp;&nbsp;&nbsp;.C&nbsp;[1&nbsp;x&nbsp;nfun]&nbsp;Bias.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Output:</span></span><br><span class=help>%&nbsp;&nbsp;y&nbsp;[1&nbsp;x&nbsp;num_data]&nbsp;Predicted&nbsp;labels.</span><br><span class=help>%&nbsp;&nbsp;dfce&nbsp;[nfun&nbsp;x&nbsp;num_data]&nbsp;Values&nbsp;of&nbsp;discriminat&nbsp;function.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Example:</span></span><br><span class=help>%&nbsp;&nbsp;trn&nbsp;=&nbsp;load('riply_trn');</span><br><span class=help>%&nbsp;&nbsp;tst&nbsp;=&nbsp;load('riply_tst');</span><br><span class=help>%&nbsp;&nbsp;gauss_model&nbsp;=&nbsp;mlcgmm(trn);</span><br><span class=help>%&nbsp;&nbsp;quad_model&nbsp;=&nbsp;bayesdf(gauss_model);</span><br><span class=help>%&nbsp;&nbsp;ypred&nbsp;=&nbsp;quadclass(tst.X,&nbsp;quad_model);</span><br><span class=help>%&nbsp;&nbsp;cerror(ypred,&nbsp;tst.y)</span><br><span class=help>%&nbsp;&nbsp;figure;&nbsp;ppatterns(trn);&nbsp;pboundary(quad_model);</span><br><span class=help>%</span><br><span class=help>%&nbsp;See&nbsp;also&nbsp;</span><br><span class=help>%&nbsp;&nbsp;QMAP,&nbsp;LIN2QUAD,&nbsp;LINCLASS</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><br><hr><span class=comment>%&nbsp;allow&nbsp;model&nbsp;to&nbsp;be&nbsp;gievn&nbsp;as&nbsp;a&nbsp;cell</span><br>model&nbsp;=&nbsp;c2s(model);<br><br>[dim,&nbsp;num_data]&nbsp;=&nbsp;size(X);<br><br>nfun&nbsp;=&nbsp;size(model.A,3);<br><br><span class=keyword>if</span>&nbsp;nfun&nbsp;==&nbsp;1,<br>&nbsp;&nbsp;<span class=comment>%&nbsp;binary&nbsp;case</span><br>&nbsp;&nbsp;dfce&nbsp;=&nbsp;sum((model.A*X).*X,1)&nbsp;+&nbsp;model.B'*X&nbsp;+&nbsp;model.C;<br>&nbsp;&nbsp;y&nbsp;=&nbsp;ones(1,num_data);<br>&nbsp;&nbsp;y(find(dfce&lt;&nbsp;0))&nbsp;=&nbsp;2;<br><span class=keyword>else</span><br>&nbsp;&nbsp;<span class=comment>%&nbsp;multi-class&nbsp;case&nbsp;</span><br>&nbsp;&nbsp;dfce&nbsp;=&nbsp;zeros(&nbsp;nfun,&nbsp;num_data&nbsp;);<br>&nbsp;&nbsp;<br>&nbsp;&nbsp;<span class=keyword>for</span>&nbsp;i=1:nfun,<br>&nbsp;&nbsp;&nbsp;&nbsp;dfce(i,:)&nbsp;=&nbsp;sum((model.A(:,:,i)*X).*X,1)&nbsp;+&nbsp;model.B(:,i)'*X&nbsp;+&nbsp;model.C(i);<br>&nbsp;&nbsp;<span class=keyword>end</span><br>&nbsp;&nbsp;<br>&nbsp;&nbsp;[dummy,y]&nbsp;=&nbsp;max(&nbsp;dfce&nbsp;);<br>&nbsp;&nbsp;<br><span class=keyword>end</span><br><br><span class=jump>return</span>;<br><span class=comment>%&nbsp;EOF</span><br></code>

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