matlab中高维数组怎么做PCA？

 

PCA需要先求数据的散布矩阵x*x'，再求其特征向量，那么随便一个400*450的图像，就是180000维，矩阵就是180000*180000，matlab无法容纳，那么通常的PCA对图像的降维，比如求eigenface是怎么实现的？难道都是很小的图像？ 修改

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吕祺，喜欢思考，爱美好的食物 修改话题经验

 

Suppose you store the images as column vectors of length NxN (the 
number of pixels in each image) and that you have M images, you'll end 
up with a matrix G (N^2 x M) : 

1 
CovMat = -------- G G^T 
M - 1 

this is what you are trying to find the eigenvalues/eigenvectors for, 
right? 

There is a trick widely used when doing PCA on sets of images, it is 
based on the fact that the (M x M) matrix: 


1 
lmCovMat = -------- G^T G 
M - 1 


has the same non-zero eigenvalues of CovMat. So what you do is to 
compute the eigenvalues and eigenvectors of this low memory covariance 
matrix and then, for the eigenvectors, compute: 

E = G lmE 

where E is a matrix containing the wanted eigenvectors and lmE is the 
matrix of the eigenvectors compouted from the lmCovMat. 

This is implemented already in the OpenCV libraries. 

Hope it helps.

 

clear
[x]=load_imgs('training');
x=x(1:100,:);
a1=x*x';
b=x'*x;
[va,p]=eig(a1/27);
[vb,q]=eig(b/27);
%b/27*vb(:,1)==q(1)*vb(:,1);

转载于:https://www.cnblogs.com/huashiyiqike/p/3406021.html