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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">GREEDYAPPX</b><td valign="baseline" align="right" class="function"><a href="../../kernels/extraction/index.html" target="mdsdir"><img border = 0 src="../../up.gif"></a></table>  <p><b>Kernel greedy data approximation.</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;[inx,Alpha,kercnt,mserr,maxerr]=...</span><br><span class=help>&nbsp;&nbsp;&nbsp;&nbsp;greedyappx(X,ker,arg,m,m2,mserr,maxerr,verb)</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;aims&nbsp;to&nbsp;select&nbsp;a&nbsp;subset&nbsp;S&nbsp;of&nbsp;input&nbsp;data&nbsp;X&nbsp;such</span><br><span class=help>&nbsp;&nbsp;that&nbsp;the&nbsp;feature&nbsp;space&nbsp;representation&nbsp;of&nbsp;X&nbsp;can&nbsp;be&nbsp;well&nbsp;</span><br><span class=help>&nbsp;&nbsp;approximated&nbsp;by&nbsp;feature&nbsp;space&nbsp;representation&nbsp;of&nbsp;S.</span><br><span class=help>&nbsp;&nbsp;The&nbsp;feature&nbsp;represenation&nbsp;of&nbsp;data&nbsp;is&nbsp;by&nbsp;the&nbsp;use&nbsp;of</span><br><span class=help>&nbsp;&nbsp;specified&nbsp;kernel&nbsp;function.</span><br><span class=help></span><br><span class=help>&nbsp;&nbsp;The&nbsp;greedy&nbsp;algortihm&nbsp;is&nbsp;used&nbsp;to&nbsp;seletect&nbsp;the&nbsp;subset&nbsp;S.&nbsp;</span><br><span class=help>&nbsp;&nbsp;The&nbsp;algorithm&nbsp;iterates&nbsp;until&nbsp;on&nbsp;of&nbsp;the&nbsp;following&nbsp;stopping&nbsp;</span><br><span class=help>&nbsp;&nbsp;conditions&nbsp;is&nbsp;achieved:</span><br><span class=help>&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;number&nbsp;of&nbsp;vectors&nbsp;of&nbsp;S&nbsp;achieves&nbsp;m&nbsp;</span><br><span class=help>&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;maximal&nbsp;reconstruction&nbsp;error&nbsp;is&nbsp;less&nbsp;than&nbsp;maxerr&nbsp;</span><br><span class=help>&nbsp;&nbsp;&nbsp;&nbsp;-&nbsp;mean&nbsp;squared&nbsp;sum&nbsp;of&nbsp;reconstruction&nbsp;errors&nbsp;less&nbsp;than&nbsp;mserr.&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.</span><br><span class=help>&nbsp;&nbsp;ker&nbsp;[string]&nbsp;Kernel&nbsp;identifier.&nbsp;See&nbsp;'help&nbsp;kernel'&nbsp;for&nbsp;more&nbsp;info.</span><br><span class=help>&nbsp;&nbsp;arg&nbsp;[...]&nbsp;Argument&nbsp;of&nbsp;selected&nbsp;kernel.</span><br><span class=help>&nbsp;&nbsp;m&nbsp;[1x1]&nbsp;Maximal&nbsp;number&nbsp;of&nbsp;vector&nbsp;used&nbsp;for&nbsp;approximation.</span><br><span class=help>&nbsp;&nbsp;p&nbsp;[1x1]&nbsp;Depth&nbsp;of&nbsp;search&nbsp;for&nbsp;the&nbsp;best&nbsp;basis&nbsp;vector.</span><br><span class=help>&nbsp;&nbsp;mserr&nbsp;[1x1]&nbsp;Desired&nbsp;mean&nbsp;sum&nbsp;of&nbsp;squared&nbsp;reconstruction&nbsp;errors.</span><br><span class=help>&nbsp;&nbsp;maxerr&nbsp;[1x1]&nbsp;Desired&nbsp;maximal&nbsp;reconstruction&nbsp;error.</span><br><span class=help>&nbsp;&nbsp;verb&nbsp;[1x1]&nbsp;If&nbsp;1&nbsp;then&nbsp;infor&nbsp;about&nbsp;process&nbsp;is&nbsp;displayed.</span><br><span class=help></span><br><span class=help>&nbsp;<span class=help_field>Output:</span></span><br><span class=help>&nbsp;&nbsp;inx&nbsp;[1&nbsp;x&nbsp;n]&nbsp;Indices&nbsp;of&nbsp;selected&nbsp;vector,&nbsp;i.e.,&nbsp;S&nbsp;=&nbsp;X(:,inx).</span><br><span class=help>&nbsp;&nbsp;Alpha&nbsp;[m&nbsp;x&nbsp;m]&nbsp;Koefficient&nbsp;of&nbsp;the&nbsp;kernel&nbsp;projection&nbsp;of&nbsp;data&nbsp;on&nbsp;the</span><br><span class=help>&nbsp;&nbsp;&nbsp;&nbsp;found&nbsp;base&nbsp;vectors,&nbsp;i.e.,&nbsp;z&nbsp;=&nbsp;Alpha*kernel(S,x,ker,arg).</span><br><span class=help>&nbsp;&nbsp;Z&nbsp;[m&nbsp;x&nbsp;num_data]&nbsp;Training&nbsp;data&nbsp;projected&nbsp;on&nbsp;the&nbsp;found&nbsp;base&nbsp;vectors.</span><br><span class=help>&nbsp;&nbsp;kercnt&nbsp;[1x1]&nbsp;Number&nbsp;of&nbsp;used&nbsp;kernel&nbsp;evaluations.</span><br><span class=help>&nbsp;&nbsp;MsErr&nbsp;[1&nbsp;x&nbsp;m]&nbsp;Sum&nbsp;of&nbsp;squared&nbsp;reconstruction&nbsp;errors&nbsp;for&nbsp;corresponding</span><br><span class=help>&nbsp;&nbsp;&nbsp;number&nbsp;of&nbsp;base&nbsp;vectors.</span><br><span class=help>&nbsp;&nbsp;MaxErr&nbsp;[1&nbsp;x&nbsp;m]&nbsp;Maximal&nbsp;squared&nbsp;reconstruction&nbsp;error&nbsp;for&nbsp;crresponding&nbsp;</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/extraction/greedykpca.html" target="mdsbody">GREEDYKPCA</a>.</span><br><span class=help></span><br></code></div>  <hr>  <b>Source:</b> <a href= "../../kernels/extraction/list/greedyappx.html">greedyappx.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> 10-dec-2004, VF, tmp(find(Errors<=0)) = -inf; added to evoid num errors.<br> 5-may-2004, VF<br> 13-mar-2004, VF<br> 10-mar-2004, VF<br> 9-mar-2004, addopted from greedyappx<br></body></html>

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