matlab中高维数组怎么做PCA？

程序员红卫技术 2022年11月7日

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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？修改举报添加评论分享 • 邀请回答

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);