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<html><head>  <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1">  <title>Contents.m</title><link rel="stylesheet" type="text/css" href="../../stpr.css"></head><body><table  border=0 width="100%" cellpadding=0 cellspacing=0><tr valign="baseline"><td valign="baseline" class="function"><b class="function">RSDE</b><td valign="baseline" align="right" class="function"><a href="../../probab/estimation/index.html" target="mdsdir"><img border = 0 src="../../up.gif"></a></table>  <p><b>Reduced Set Density Estimator.</b></p>  <hr><div class='code'><code><span class=help></span><br><span class=help>&nbsp;<span class=help_field>Synopsis:</span></span><br><span class=help>&nbsp;&nbsp;model&nbsp;=&nbsp;rsde(X,options)</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;implements&nbsp;the&nbsp;Reduced&nbsp;Set&nbsp;Density&nbsp;Estimator&nbsp;</span><br><span class=help>&nbsp;&nbsp;[<a href="../../references.html#Girol03" title = "" >Girol03</a>]&nbsp;which&nbsp;provides&nbsp;kernel&nbsp;density&nbsp;estimate&nbsp;optimal&nbsp;</span><br><span class=help>&nbsp;&nbsp;in&nbsp;the&nbsp;L2&nbsp;sense.&nbsp;The&nbsp;density&nbsp;is&nbsp;modeled&nbsp;as&nbsp;the&nbsp;weighted&nbsp;sum&nbsp;</span><br><span class=help>&nbsp;&nbsp;of&nbsp;Gaussians&nbsp;(RBF&nbsp;kernel)&nbsp;centered&nbsp;in&nbsp;seleceted&nbsp;subset&nbsp;of&nbsp;</span><br><span class=help>&nbsp;&nbsp;training&nbsp;data.&nbsp;</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;X&nbsp;[dim&nbsp;x&nbsp;num_data]&nbsp;Input&nbsp;data&nbsp;sample.</span><br><span class=help>&nbsp;&nbsp;options&nbsp;[struct]&nbsp;Control&nbsp;parameters:</span><br><span class=help>&nbsp;&nbsp;&nbsp;.arg&nbsp;[1x1]&nbsp;Standard&nbsp;deviation&nbsp;of&nbsp;the&nbsp;Gaussian&nbsp;kernel.</span><br><span class=help>&nbsp;&nbsp;&nbsp;.solver&nbsp;[string]&nbsp;Quadratic&nbsp;Programming&nbsp;solver&nbsp;(default&nbsp;'quadprog');</span><br><span class=help></span><br><span class=help>&nbsp;<span class=help_field>Output:</span></span><br><span class=help>&nbsp;&nbsp;model&nbsp;[struct]&nbsp;Output&nbsp;density&nbsp;model:</span><br><span class=help>&nbsp;&nbsp;&nbsp;.Alpha&nbsp;[nsv&nbsp;x&nbsp;1]&nbsp;Weights&nbsp;of&nbsp;the&nbsp;kernel&nbsp;functions.</span><br><span class=help>&nbsp;&nbsp;&nbsp;.sv.X&nbsp;[dim&nbsp;x&nbsp;nsv]&nbsp;Selected&nbsp;centers&nbsp;of&nbsp;kernel&nbsp;functions.</span><br><span class=help>&nbsp;&nbsp;&nbsp;.nsv&nbsp;[1x1]&nbsp;Number&nbsp;of&nbsp;selected&nbsp;centers.</span><br><span class=help>&nbsp;&nbsp;&nbsp;.options.arg&nbsp;=&nbsp;options.arg.</span><br><span class=help>&nbsp;&nbsp;&nbsp;.options.ker&nbsp;=&nbsp;'rbf'</span><br><span class=help>&nbsp;&nbsp;&nbsp;</span><br><span class=help>&nbsp;<span class=help_field>Example:</span></span><br><span class=help>&nbsp;&nbsp;gnd&nbsp;=&nbsp;struct('Mean',[-2&nbsp;3],'Cov',[1&nbsp;0.5],'Prior',[0.4&nbsp;0.6]);</span><br><span class=help>&nbsp;&nbsp;sample&nbsp;=&nbsp;gmmsamp(&nbsp;gnd,&nbsp;200&nbsp;);</span><br><span class=help>&nbsp;&nbsp;figure;&nbsp;hold&nbsp;on;&nbsp;ppatterns(sample.X);</span><br><span class=help>&nbsp;&nbsp;plot([-4:0.1:8],&nbsp;pdfgmm([-4:0.1:8],gnd),'r');</span><br><span class=help>&nbsp;&nbsp;model&nbsp;=&nbsp;rsde(sample.X,struct('arg',0.7));</span><br><span class=help>&nbsp;&nbsp;x&nbsp;=&nbsp;linspace(-4,8,100);</span><br><span class=help>&nbsp;&nbsp;plot(x,kernelproj(x,model),'g');&nbsp;</span><br><span class=help>&nbsp;&nbsp;ppatterns(model.sv.X,'ob',13);</span><br><span class=help></span><br><span class=help>&nbsp;<span class=also_field>See also </span><span class=also></span><br><span class=help><span class=also>&nbsp;&nbsp;<a href = "../../kernels/kernelproj.html" target="mdsbody">KERNELPROJ</a>.</span><br><span class=help></span><br></code></div>  <hr>  <b>Source:</b> <a href= "../../probab/estimation/list/rsde.html">rsde.m</a>  <p><b class="info_field">About: </b>  Statistical Pattern Recognition Toolbox<br> (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac<br> <a href="http://www.cvut.cz">Czech Technical University Prague</a><br> <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a><br> <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a><br>  <p><b class="info_field">Modifications: </b> <br> 17-sep-2004, VF, revised<br></body></html>
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