Metrics for Matrices similarity

Dear all, I have made a process that makes approxmation of a source matrix.

Every approximated matrix contains error which usually are extreme values (compares to the source). I have noticed that when sme approximation start looking the same then I am getting really close the source image.

That I want to ask you if you know some mathematical ways to measure similaritis in two approximated-matrices. I have used already the corrcoef and it results goosd results but I also want to check other metric.

I wuld like to thank you in advance for your help B.R Alex

Answer 1

[bym]

you can try using their eigenvalues:

x = norm(eig(a)-eig(b)); % a & b are your 2 matricies

[Alex]

very good answer :)

could you please give few more hints why you thought about this method?

[bym]

Initially, I was thinking of using SVD which comes up a lot in the literature when approximating a matrix. I just thought the eig method would be easier

[Alex]

One more thing: How I should interpret the results of the

x = norm(eig(X3)-eig(Y3))

the larger the number larger similarity is?

B.R

Alex

[Andrei Bobrov]

conversely

[Alex]

what does it mean?

[bym]

it means the lower the value the greater the similarity

[Shima Khatiri]

Will it work for a non-square matrix? Because I'm receiving error: For standard eigenproblem EIG(A), A must be square. How can we compare two matrices with different sizes and non-square?

[Christine Tobler]

Hi Shima,

It's usually better to start a new post than reviving an old one. I'm not sure of the context for the original post, but I'd typically measure the difference between matrices using

 norm(A-B)

which works for non-square matrices, too.

[Shanelle Clarke]

I've found that Christine's answer ( norm(A-B)) works better for me, since MATLAB doesn't always report the eig(A) and eig(B) in the same order.