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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">KPCA</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 Principal Component Analysis.</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> model = kpca(X)</span><br><span class=help> model = kpca(X,options)</span><br><span class=help></span><br><span class=help> <span class=help_field>Description:</span></span><br><span class=help> This function is implementation of Kernel Principal Component </span><br><span class=help> Analysis (KPCA) [<a href="../../references.html#Schol98b" title = "" >Schol98b</a>]. The input data X are non-linearly</span><br><span class=help> mapped to a new high dimensional space induced by prescribed</span><br><span class=help> kernel function. The PCA is applied on the non-linearly mapped </span><br><span class=help> data. The result is a model describing non-linear data projection.</span><br><span class=help> See 'help kernelproj' for info how to project data.</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] Training data.</span><br><span class=help> </span><br><span class=help> options [struct] Decribes kernel and output dimension:</span><br><span class=help> .ker [string] Kernel identifier (see 'help kernel'); </span><br><span class=help> (default 'linear').</span><br><span class=help> .arg [1 x narg] kernel argument; (default 1).</span><br><span class=help> .new_dim [1x1] Output dimension (number of used principal </span><br><span class=help> components); (default dim).</span><br><span class=help></span><br><span class=help> <span class=help_field>Output:</span></span><br><span class=help> model [struct] Kernel projection:</span><br><span class=help> .Alpha [num_data x new_dim] Multipliers.</span><br><span class=help> .b [new_dim x 1] Bias.</span><br><span class=help> .sv.X [dim x num_data] Training vectors.</span><br><span class=help> </span><br><span class=help> .nsv [1x1] Number of training data.</span><br><span class=help> .eigval [1 x num_data] Eigenvalues of centered kernel matrix.</span><br><span class=help> .mse [1x1] Mean square representation error of maped data.</span><br><span class=help> .MsErr [dim x 1] MSE with respect to used basis vectors;</span><br><span class=help> mse=MsErr(new_dim).</span><br><span class=help> .kercnt [1x1] Number of used kernel evaluations.</span><br><span class=help> .options [struct] Copy of used options.</span><br><span class=help> .cputime [1x1] CPU time used for training.</span><br><span class=help></span><br><span class=help> <span class=help_field>Example:</span></span><br><span class=help> X = gencircledata([1;1],5,250,1);</span><br><span class=help> model = kpca( X, struct('ker','rbf','arg',4,'new_dim',2));</span><br><span class=help> XR = kpcarec( X, model );</span><br><span class=help> figure; </span><br><span class=help> ppatterns( X ); ppatterns( XR, '+r' );</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/kernelproj.html" target="mdsbody">KERNELPROJ</a>, <a href = "../../linear/extraction/pca.html" target="mdsbody">PCA</a>, <a href = "../../kernels/extraction/gda.html" target="mdsbody">GDA</a>.</span><br><span class=help> </span><br></code></div> <hr> <b>Source:</b> <a href= "../../kernels/extraction/list/kpca.html">kpca.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> 4-may-2004, VF<br> 10-july-2003, VF, computation of kercnt added<br> 22-jan-2003, VF<br> 11-july-2002, VF, mistake "Jt=zeros(N,L)/N" repared <br> (reported by SH_Srinivasan@Satyam.com).<br> 5-July-2001, V.Franc, comments changed<br> 20-dec-2000, V.Franc, algorithm was implemented<br></body></html>⌨️ 快捷键说明
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