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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>redquadh.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>red_model&nbsp;</span>=&nbsp;<span class=defun_name>redquadh</span>(<span class=defun_in>model</span>)<br><span class=h1>%&nbsp;REDQUADH&nbsp;reduced&nbsp;SVM&nbsp;classifier&nbsp;with&nbsp;homogeneous&nbsp;quadratic&nbsp;kernel.</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Synopsis:</span></span><br><span class=help>%&nbsp;&nbsp;red_model&nbsp;=&nbsp;redquadh(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;It&nbsp;uses&nbsp;reduced&nbsp;set&nbsp;techique&nbsp;(Burges)&nbsp;to&nbsp;compute&nbsp;</span><br><span class=help>%&nbsp;&nbsp;simpler&nbsp;SVM&nbsp;binary&nbsp;rule&nbsp;with&nbsp;homogeneous&nbsp;quadratic&nbsp;kernel&nbsp;(x'*y)^2.</span><br><span class=help>%&nbsp;&nbsp;</span><br><span class=help>%&nbsp;<span class=help_field>Input:</span></span><br><span class=help>%&nbsp;&nbsp;model.Alpha&nbsp;[nsv&nbsp;x&nbsp;1]&nbsp;Weights&nbsp;of&nbsp;kernel&nbsp;expansion.</span><br><span class=help>%&nbsp;&nbsp;model.b&nbsp;[scalar]&nbsp;Bias.</span><br><span class=help>%&nbsp;&nbsp;model.sv.X&nbsp;[dim&nbsp;x&nbsp;nsv]&nbsp;Support&nbsp;vectors.</span><br><span class=help>%&nbsp;&nbsp;model.options.ker&nbsp;=&nbsp;'poly'</span><br><span class=help>%&nbsp;&nbsp;model.options.arg&nbsp;=&nbsp;[2&nbsp;0]</span><br><span class=help>%</span><br><span class=help>%&nbsp;<span class=help_field>Output:</span></span><br><span class=help>%&nbsp;&nbsp;red_model.Alpha&nbsp;[new_nsv&nbsp;x&nbsp;1]&nbsp;New&nbsp;weights.</span><br><span class=help>%&nbsp;&nbsp;red_model.b&nbsp;[scalar]&nbsp;Bias.</span><br><span class=help>%&nbsp;&nbsp;red_model.sv.X&nbsp;[dim&nbsp;x&nbsp;new_nsv]&nbsp;New&nbsp;"support&nbsp;vectors".</span><br><span class=help>%&nbsp;&nbsp;...</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;model&nbsp;=&nbsp;smo(trn,{'ker','poly','arg',[2&nbsp;0],'C',10});</span><br><span class=help>%&nbsp;&nbsp;red_model&nbsp;=&nbsp;redquadh(&nbsp;model&nbsp;);</span><br><span class=help>%&nbsp;&nbsp;figure;&nbsp;ppatterns(trn);&nbsp;psvm(model);</span><br><span class=help>%&nbsp;&nbsp;figure;&nbsp;ppatterns(trn);&nbsp;psvm(red_model);</span><br><span class=help>%</span><br><hr><span class=help1>%&nbsp;<span class=help1_field>Modifications:</span></span><br><span class=help1>%&nbsp;28-nov-2003,&nbsp;VF</span><br><br><hr>dim=size(model.sv.X,1);<br>nsv&nbsp;=&nbsp;model.nsv;<br><br>S&nbsp;=&nbsp;zeros(dim,dim);<br><br><span class=keyword>for</span>&nbsp;i=1:dim,<br>&nbsp;&nbsp;<span class=keyword>for</span>&nbsp;j=i:dim,<br>&nbsp;&nbsp;&nbsp;&nbsp;S(i,j)&nbsp;=&nbsp;(model.sv.X(i,:).*model.sv.X(j,:)&nbsp;)*model.Alpha(:);<br>&nbsp;&nbsp;&nbsp;&nbsp;S(j,i)&nbsp;=&nbsp;S(i,j);<br>&nbsp;&nbsp;<span class=keyword>end</span><br><span class=keyword>end</span><br><br>[V,D]&nbsp;=&nbsp;eig(S);<br>D=real(diag(D));<br>[dummy,inx]&nbsp;=&nbsp;sort(-abs(D));<br>D=D(inx);<br>V=V(:,inx);<br><br>inx&nbsp;=&nbsp;find(D&nbsp;~=&nbsp;0);<br><br>red_model.nsv&nbsp;=&nbsp;length(inx);<br>red_model.Alpha&nbsp;=&nbsp;zeros(red_model.nsv,1);<br>red_model.b&nbsp;=&nbsp;model.b;<br>red_model.sv.X&nbsp;=&nbsp;zeros(dim,red_model.nsv);<br>red_model.options&nbsp;=&nbsp;model.options;<br>red_model.classifier&nbsp;=&nbsp;<span class=quotes>'svmclass'</span>;<br>red_model.eigval&nbsp;=&nbsp;D(inx);<br><br>cnt&nbsp;=&nbsp;0;<br><span class=keyword>for</span>&nbsp;i=inx(:)',<br>&nbsp;&nbsp;cnt&nbsp;=&nbsp;cnt+1;<br>&nbsp;&nbsp;red_model.sv.X(:,cnt)&nbsp;=&nbsp;V(:,i);<br>&nbsp;&nbsp;red_model.Alpha(cnt)&nbsp;=&nbsp;D(i)/(red_model.sv.X(:,cnt)'*red_model.sv.X(:,cnt));<br><span class=keyword>end</span><br><br><span class=jump>return</span>;<br><br><br></code>

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