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<H1 class=ContentTitle><STRONG>PCA算法程序</STRONG></H1>
<H2 class=ContentAuthor>作者:dinga 日期:2007-04-17</H2></DIV>
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id=logPanel>程序说明：y = pca(mixedsig)，程序中mixedsig为 n*T 阶混合数据矩阵，n为信号个数，T为采样点数, y为 m*T 阶主分量矩阵。<BR><BR><SPAN
style="COLOR: red">程序设计步骤</SPAN>：<BR>1、去均值<BR>2、计算协方差矩阵及其特征值和特征向量<BR>3、计算协方差矩阵的特征值大于阈值的个数<BR>4、降序排列特征值<BR>5、去掉较小的特征值<BR>6、去掉较大的特征值(<SPAN
style="COLOR: blue">一般没有这一步</SPAN>）<BR>7、合并选择的特征值<BR>8、选择相应的特征值和特征向量<BR>9、计算白化矩阵<BR>10、提取主分量<BR><BR>
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<DIV class=UBBTitle><IMG style="MARGIN: 0px 2px -3px 0px" alt=程序代码
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<DIV
class=UBBContent><BR>%程序说明：y = pca(mixedsig)，程序中mixedsig为 n*T 阶混合数据矩阵，n为信号个数，T为采样点数<BR>% y为 m*T 阶主分量矩阵。<BR><BR>function y = pca(mixedsig)<BR>if nargin == 0<BR> error('You must supply the mixed data as input argument.');<BR>end<BR>if length(size(mixedsig))>2<BR> error('Input data can not have more than two dimensions. ');<BR>end<BR>if any(any(isnan(mixedsig)))<BR> error('Input data contains NaN''s.');<BR>end<BR><BR>%——————————————去均值————————————<BR>meanValue = mean(mixedsig')';<BR>mixedsig = mixedsig - meanValue * ones(1,size(meanValue,2));<BR>[Dim,NumofSampl] = size(mixedsig);<BR>oldDimension = Dim;<BR>fprintf('Number of signals: %d\n',Dim);<BR>fprintf('Number of samples: %d\n',NumofSampl);<BR>fprintf('Calculate PCA...');<BR>firstEig = 1;<BR>lastEig = Dim;<BR>covarianceMatrix = cov(mixedsig',1); %计算协方差矩阵<BR>[E,D] = eig(covarianceMatrix); %计算协方差矩阵的特征值和特征向量<BR><BR>%———计算协方差矩阵的特征值大于阈值的个数lastEig———<BR>rankTolerance = 1e-5;<BR>maxLastEig = sum(diag(D)) > rankTolerance;<BR>lastEig = maxLastEig;<BR><BR>%——————————降序排列特征值——————————<BR>eigenvalues = flipud(sort(diag(D)));<BR><BR>%—————————去掉较小的特征值——————————<BR>if lastEig < oldDimension<BR> lowerLimitValue = (eigenvalues(lastEig) + eigenvalues(lastEig + 1))/2;<BR>else<BR> lowerLimitValue = eigenvalues(oldDimension) - 1;<BR>end<BR>lowerColumns = diag(D) > lowerLimitValue;<BR><BR>%—————去掉较大的特征值(一般没有这一步)——————<BR>if firstEig > 1<BR> higherLimitValue = (eigenvalues(firstEig - 1) + eigenvalues(firstEig))/2;<BR>else<BR> higherLimitValue = eigenvalues(1) + 1;<BR>end<BR>higherColumns = diag(D) < higherLimitValue;<BR><BR>%—————————合并选择的特征值——————————<BR>selectedColumns =lowerColumns & higherColumns;<BR><BR>%—————————输出处理的结果信息—————————<BR>fprintf('Selected[ %d ] dimensions.\n',sum(selectedColumns));<BR>fprintf('Smallest remaining (non-zero) eigenvalue[ %g ]\n',eigenvalues(lastEig));<BR>fprintf('Largest remaining (non-zero) eigenvalue[ %g ]\n',eigenvalues(firstEig));<BR>fprintf('Sum of removed eigenvalue[ %g ]\n',sum(diag(D) .* (~selectedColumns)));<BR><BR>%———————选择相应的特征值和特征向量———————<BR>E = selcol(E,selectedColumns);<BR>D = selcol(selcol(D,selectedColumns)',selectedColumns);<BR><BR>%——————————计算白化矩阵———————————<BR>whiteningMatrix = inv(sqrt(D)) * E';<BR>dewhiteningMatrix = E * sqrt(D);<BR><BR>%——————————提取主分量————————————<BR>y = whiteningMatrix * mixedsig;<BR><BR>%——————————行选择子程序———————————<BR>function newMatrix = selcol(oldMatrix,maskVector)<BR>if size(maskVector,1)~ = size(oldMatrix,2)<BR> error('The mask vector and matrix are of uncompatible size.');<BR>end<BR>numTaken = 0;<BR>for i = 1:size(maskVector,1)<BR> if maskVector(i,1) == 1<BR> takingMask(1,numTaken + 1) == i;<BR> numTaken = numTaken + 1;<BR> end<BR>end<BR>newMatrix = oldMatrix(:,takingMask);<BR></DIV></DIV><BR><BR></DIV>
<DIV class=Content-body>[本日志由 dinga 于 2007-04-17 09:36 AM 编辑]<BR><IMG
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src="PCA算法程序 - Dinga's Blog.files/tag.gif"><STRONG>Tags:</STRONG> <A
href="http://www.dinga.cn/default.asp?tag=PCA">PCA</A><A style="DISPLAY: none"
href="http://technorati.com/tag/PCA" rel=tag>PCA</A> <A
href="http://www.dinga.cn/default.asp?tag=%E7%AE%97%E6%B3%95">算法</A><A
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<A href="http://www.dinga.cn/default.asp?tag=matlab">matlab</A><A
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<DIV class=ContentBRight></DIV>评论: 5 | 引用: 0 | 查看次数: 2529 </DIV></DIV></DIV><A
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<DIV class=commenttop><A href="javascript:addQuote('betty','commcontent_1263')"
name=comm_1263><IMG style="MARGIN: 0px 4px -3px 0px" alt=""
src="PCA算法程序 - Dinga's Blog.files/icon_quote.gif" border=0></A><A
href="http://www.dinga.cn/member.asp?action=view&memName=betty"><STRONG>betty</STRONG></A>
<SPAN class=commentinfo>[2008-03-19 10:18 AM]</SPAN></DIV>
<DIV class=commentcontent id=commcontent_1263>没有定义mixdsig。。</DIV></DIV>
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<DIV class=commenttop><A
href="javascript:addQuote('hihello','commcontent_1204')" name=comm_1204><IMG
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src="PCA算法程序 - Dinga's Blog.files/icon_quote.gif" border=0></A><A
href="http://www.dinga.cn/member.asp?action=view&memName=hihello"><STRONG>hihello</STRONG></A>
<SPAN class=commentinfo>[2007-12-08 00:31 AM]</SPAN></DIV>
<DIV class=commentcontent id=commcontent_1204>takingMask这个函数没有定义</DIV></DIV>
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