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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> <span class=help_field>Synopsis:</span></span><br><span class=help> [Sel_inx,Alpha,Z,Kercnt,MsErrors,MaxErrors] = ...</span><br><span class=help> greedyappx(X,Ker,Arg,M,P,MsErr,Maxerr,Verb) </span><br><span class=help></span><br><span class=help> <span class=help_field>Description:</span></span><br><span class=help> The input column vectors are assumed to be represented</span><br><span class=help> in a kernel feature space given by (ker,arg) (see help kernel).</span><br><span class=help> This function aims to select a subset X(:,Sel_inx) such</span><br><span class=help> that linear span of X(:,Sel_inx) in the feature space </span><br><span class=help> approximates well the linear span of X in the feature space.</span><br><span class=help> The vectors are selected such that the mean square reconstruction</span><br><span class=help> error in the feature space (the same objective as has Kernel PCA) </span><br><span class=help> is minimized by greedy algorithm. The algorithm selects vectors</span><br><span class=help> until on of the following stopping conditions is achieved:</span><br><span class=help> - number of vectors achieves m </span><br><span class=help> - maximal reconstruction error drops below maxerr </span><br><span class=help> - mean squared sum of reconstruction errors less than mserr. </span><br><span class=help> </span><br><span class=help> The images of X(:,Inx_sel) in the features form a basis.</span><br><span class=help> The projection of input vector x into the basis is done by</span><br><span class=help> z = Alpha*kernel(x,X(:,Sel_inx),Ker,Arg)</span><br><span class=help></span><br><span class=help> For more info refer to V.Franc: Optimization Algorithms for Kernel </span><br><span class=help> Methods. Research report. CTU-CMP-2005-22. CTU FEL Prague. 2005.</span><br><span class=help> ftp://cmp.felk.cvut.cz/pub/cmp/articles/franc/Franc-PhD.pdf .</span><br><span class=help></span><br><span class=help> <span class=help_field>Input:</span></span><br><span class=help> X [Dim x Num_data] Input data.</span><br><span class=help> Ker [string] Kernel identifier. See help of KERNEL for more info.</span><br><span class=help> Arg [...] Argument of selected kernel.</span><br><span class=help> M [1x1] Maximal number of vector used for approximation.</span><br><span class=help> P [1x1] Depth of search for each basis vector.</span><br><span class=help> MsErr [1x1] Desired mean sum of squared reconstruction errors.</span><br><span class=help> MaxErr [1x1] Desired maximal reconstruction error.</span><br><span class=help> Verb [1x1] If 1 then infor about process is displayed.</span><br><span class=help></span><br><span class=help> <span class=help_field>Output:</span></span><br><span class=help> Sel_inx [1 x M] Indices of selected vector, i.e., S = X(:,Sel_inx).</span><br><span class=help> Alpha [M x M] Defines projection into the found basis (see above).</span><br><span class=help> Z [M x Num_data] Training data projected into the found basis.</span><br><span class=help> Kercnt [1 x 1] Number of used kernel evaluations.</span><br><span class=help> MsErrors [1 x M] Mean square reconstruction error wrt to selected </span><br><span class=help> basis vectors. MsErr(end) is the resulting error.</span><br><span class=help> MaxErrors [1 x M] Maximal squared reconstruction error (of the worst</span><br><span class=help> input example) wrt. selcetd basis vectors.</span><br><span class=help></span><br><span class=help> <span class=help_field>Example:</span></span><br><span class=help> type greedykpca</span><br><span class=help></span><br><span class=help> <span class=also_field>See also </span><span class=also></span><br><span class=help><span class=also> <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> 09-sep-2005, VF<br> 12-feb-2005, VF, New help made<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>⌨️ 快捷键说明
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