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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/REC-html40/loose.dtd"><html><head> <title>Description of lda</title> <meta name="keywords" content="lda"> <meta name="description" content="lda: Linear discriminant analysis"> <meta http-equiv="Content-Type" content="text/html; charset=big5"> <meta name="generator" content="m2html © 2003 Guillaume Flandin"> <meta name="robots" content="index, follow"> <link type="text/css" rel="stylesheet" href="../m2html.css"></head><body><a name="_top"></a><div><a href="../index.html">Home</a> > <a href="index.html">dcpr</a> > lda.m</div><!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td><td align="right"><a href="index.html">Index for dcpr <img alt=">" border="0" src="../right.png"></a></td></tr></table>--><h1>lda</h1><h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>lda: Linear discriminant analysis</strong></div><h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="box"><strong>function [DS2, discrimVec, eigValues] = lda(DS, discrimVecNum) </strong></div><h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="fragment"><pre class="comment">lda: Linear discriminant analysis
Usage:
[DS2, discrimVec, eigValues] = lda(DS, discrimVecNum)
DS: input data set.
Please try "DS=prData('iris')" to get an example of DS.
discrimVecNum: No. of discriminant vectors
DS2: output data set, with new feature vectors
Reference:
J. Duchene and S. Leclercq, "An Optimal Transformation for
Discriminant Principal Component Analysis," IEEE Trans. on
Pattern Analysis and Machine Intelligence,
Vol. 10, No 6, November 1988
Type "lda" for a self-demo.</pre></div><!-- crossreference --><h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>This function calls:<ul style="list-style-image:url(../matlabicon.gif)"><li><a href="classSize.html" class="code" title="function [class, count] = classSize(DS, plotOpt)">classSize</a> classSize: Class sizes for a sample data set</li><li><a href="dcprDataPlot.html" class="code" title="function dcprDataPlot(DS, plotTitle, displayAnnotation)">dcprDataPlot</a> dcprDataPlot: Plot of 2D data for data clustering or pattern recognition</li><li><a href="knnrLoo.html" class="code" title="function [recogRate, computed, nearestIndex] = knnrLoo(DS, k, plotOpt)">knnrLoo</a> knnrLoo: Leave-one-out recognition rate of KNNR</li><li><a href="prData.html" class="code" title="function [DS, TS]=prData(dataName)">prData</a> prData: Various data set for PR</li></ul>This function is called by:<ul style="list-style-image:url(../matlabicon.gif)"><li><a href="ldaKnnrLoo.html" class="code" title="function recogRate=ldaKnnrLoo(DS, maxDim, plotOpt)">ldaKnnrLoo</a> ldaKnnrLoo: LDA analysis using KNNR and LOO</li></ul><!-- crossreference --><h2><a name="_subfunctions"></a>SUBFUNCTIONS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><ul style="list-style-image:url(../matlabicon.gif)"><li><a href="#_sub1" class="code">function selfdemo</a></li></ul><h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2><div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [DS2, discrimVec, eigValues] = lda(DS, discrimVecNum)</a>0002 <span class="comment">%lda: Linear discriminant analysis</span>0003 <span class="comment">% Usage:</span>0004 <span class="comment">% [DS2, discrimVec, eigValues] = lda(DS, discrimVecNum)</span>0005 <span class="comment">% DS: input data set.</span>0006 <span class="comment">% Please try "DS=prData('iris')" to get an example of DS.</span>0007 <span class="comment">% discrimVecNum: No. of discriminant vectors</span>0008 <span class="comment">% DS2: output data set, with new feature vectors</span>0009 <span class="comment">%</span>0010 <span class="comment">% Reference:</span>0011 <span class="comment">% J. Duchene and S. Leclercq, "An Optimal Transformation for</span>0012 <span class="comment">% Discriminant Principal Component Analysis," IEEE Trans. on</span>0013 <span class="comment">% Pattern Analysis and Machine Intelligence,</span>0014 <span class="comment">% Vol. 10, No 6, November 1988</span>0015 <span class="comment">%</span>0016 <span class="comment">% Type "lda" for a self-demo.</span>0017 0018 <span class="comment">% Roger Jang, 19990829, 20030607</span>0019 0020 <span class="keyword">if</span> nargin<1, <a href="#_sub1" class="code" title="subfunction selfdemo">selfdemo</a>; <span class="keyword">return</span>; <span class="keyword">end</span>0021 <span class="keyword">if</span> ~isstruct(DS)0022 fprintf(<span class="string">'Please try "DS=prData(''iris'')" to get an example of DS.\n'</span>);0023 error(<span class="string">'The input DS should be a structure variable!'</span>);0024 <span class="keyword">end</span>0025 <span class="keyword">if</span> nargin<2, discrimVecNum=size(DS.input,1); <span class="keyword">end</span>0026 0027 <span class="comment">% ====== Initialization</span>0028 m = size(DS.input,1); <span class="comment">% Dimension of data point</span>0029 n = size(DS.input,2); <span class="comment">% No. of data point</span>0030 A = DS.input;0031 <span class="keyword">if</span> size(DS.output, 1)==1 <span class="comment">% Crisp output</span>0032 classLabel = DS.output;0033 [diffClassLabel, <a href="classSize.html" class="code" title="function [class, count] = classSize(DS, plotOpt)">classSize</a>] = elementCount(classLabel);0034 classNum = length(diffClassLabel);0035 mu = mean(A, 2);0036 0037 <span class="comment">% ====== Compute B and W</span>0038 <span class="comment">% ====== B: between-class scatter matrix</span>0039 <span class="comment">% ====== W: within-class scatter matrix</span>0040 <span class="comment">% M = \sum_k m_k*mu_k*mu_k^T</span>0041 M = zeros(m, m);0042 <span class="keyword">for</span> i = 1:classNum,0043 index = find(classLabel==diffClassLabel(i));0044 classMean = mean(A(:, index), 2);0045 M = M + length(index)*classMean*classMean';0046 <span class="keyword">end</span>0047 W = A*A'-M;0048 B = M-n*mu*mu';0049 <span class="keyword">else</span> <span class="comment">% Potential fuzzy output</span>0050 <span class="keyword">end</span>0051 0052 <span class="comment">% ====== Find the best discriminant vectors</span>0053 invW = inv(W);0054 Q = invW*B;0055 0056 D = [];0057 <span class="keyword">for</span> i = 1:discrimVecNum0058 [eigVec, eigVal] = eig(Q);0059 [eigValues(i), index] = max(diag(eigVal)); 0060 D = [D, eigVec(:, index)]; <span class="comment">% Each col of D is a eigenvector</span>0061 Q = (eye(m)-invW*D*inv(D'*invW*D)*D')*invW*B;0062 <span class="keyword">end</span>0063 DS2=DS;0064 DS2.input = D(:,1:discrimVecNum)'*A; 0065 discrimVec = D;0066 0067 <span class="comment">% ====== Self demo</span>0068 <a name="_sub1" href="#_subfunctions" class="code">function selfdemo</a>0069 <span class="comment">% ====== Self demo using IRIS dataset</span>0070 DS=<a href="prData.html" class="code" title="function [DS, TS]=prData(dataName)">prData</a>(<span class="string">'iris'</span>);0071 DS2=feval(mfilename, DS);0072 figure; <a href="dcprDataPlot.html" class="code" title="function dcprDataPlot(DS, plotTitle, displayAnnotation)">dcprDataPlot</a>(DS2); xlabel(<span class="string">'Input 1'</span>); ylabel(<span class="string">'Input 2'</span>);0073 DS2.input=DS2.input(3:4, :);0074 figure; <a href="dcprDataPlot.html" class="code" title="function dcprDataPlot(DS, plotTitle, displayAnnotation)">dcprDataPlot</a>(DS2); xlabel(<span class="string">'Input 3'</span>); ylabel(<span class="string">'Input 4'</span>);0075 <span class="comment">% ====== Leave-one-out errors after using LDA for dimension reduction</span>0076 DS=<a href="prData.html" class="code" title="function [DS, TS]=prData(dataName)">prData</a>(<span class="string">'iris'</span>);0077 recogRate = <a href="knnrLoo.html" class="code" title="function [recogRate, computed, nearestIndex] = knnrLoo(DS, k, plotOpt)">knnrLoo</a>(DS); 0078 fprintf(<span class="string">'Full data ===> LOO recog. rate = %g%%\n'</span>, 100*recogRate);0079 DS2 = feval(mfilename, DS);0080 <span class="keyword">for</span> i = 1:40081 DS3=DS2; DS3.input=DS3.input(1:i, :);0082 [recogRate(i), hitIndex] = <a href="knnrLoo.html" class="code" title="function [recogRate, computed, nearestIndex] = knnrLoo(DS, k, plotOpt)">knnrLoo</a>(DS3);0083 fprintf(<span class="string">'LDA dim = %d ===> LOO recog. rate = %g%%\n'</span>, i, 100*recogRate(i));0084 <span class="keyword">end</span></pre></div><hr><address>Generated on Thu 30-Oct-2008 12:53:56 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address></body></html>⌨️ 快捷键说明
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