pca主成分分析Matlab源码

1、function pc, score, latent, tsquare = princomp(x);% PRINCOMP Principal Component Analysis (centered and scaled data).% PC, SCORE, LATENT, TSQUARE = PRINCOMP(X) takes a data matri x X and % returns the principal components in PC, the so-called Z-scores in SCORE S,% the eigenvalues of the covariance m

2、atrix of X in LATENT, and Hotelling 's% T-squared statistic for each data point in TSQUARE.% Reference: J. Edward Jackson, A User's Guide to Principal Components% John Wiley & Sons, Inc. 1991 pp. 1-25.% B. Jones 3-17-94% Copyright 1993-2002 The MathWorks, Inc.% $Revision: 2.9 $ $Date: 20

3、02/01/17 21:31:45 $m,n = size(x);r = min(m-1,n);%avg = mean(x);%得到矩阵的规模，m行，n列% max possible rank of x该矩阵最大的秩不能超过列数，也不能超过行数减 1% 求每一列的均值，付给一个 n 维行向量centerx = (x - avg(ones(m,1),:);% x的每个元素减去该列的均值，% 使样本点集合重心与坐标原点重合U,latent,pc = svd(centerx./sqrt(m-1),0);% “经济型”的奇异值分解score = centerx*pc;% 得分矩阵即为原始矩阵乘主成分矩

4、阵if nargout < 3, return ; endlate nt = diag(late nt)42;%将奇异值矩阵转化为一个向量if (r<N)latent = latent(1:r); zeros(n-r,1);score(:,r+1:end) = 0; end if nargout < 4, return ; end tmp = sqrt(diag(1./latent(1:r)*score(:,1:r)' tsquare = sum(tmp.*tmp)'主成分分析 Matlab 版主成份分析*function main() %* %读入文件数据X

5、=load('data.txt');%=方=法 1:求标准化后的协差矩阵 ,再求特征根和特征向量 %标准化处理p,n=size(X);for j=1:nmju(j)=mean(X(:,j); sigma(j)=sqrt(cov(X(:,j); end for i=1:pfor j=1:n Y(i,j)=(X(i,j)-mju(j)/sigma(j);endendsigmaY=cov(Y);%求 X 标准化的协差矩阵的特征根和特征向量 T,lambda=eig(sigmaY);disp(' 特征根 ( 由小到大 ):'); disp(lambda);disp(&#

6、39; 特征向量 :');disp(T);%方差贡献率 ; 累计方差贡献率 Xsum=sum(sum(lambda,2),1); for i=1:nfai(i)=lambda(i,i)/Xsum;endfor i=1:npsai(i)= sum(sum(lambda(1:i,1:i),2),1)/Xsum; enddisp(' 方差贡献率 :'); disp(fai);disp(' 累计方差贡献率 :'); disp(psai);%综合评价 略%+=方法2:求X的相关系数矩阵,再求特征根和特征向量 %X勺标准化的协方差矩阵就是X的相关系数矩阵R=corrcoef(X);%求 X相关系数矩阵的特征根和特征向量TR,lambd