MATLAB: Metrics for Matrices similarity

metrics for 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

Best Answer

you can try using their eigenvalues:

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

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MATLAB: How to define nuclear norm in matlab

What is difficult to program? A quick search online suggests it is the L-1 norm of either the vector of singular values, or of the vector of eigenvalues. It depends if your matrix is square or not.

This is simple to write however. Use eig (or svd) as you wish. Then call norm (with the correct norm) and you are done. WTP? Thus it can be written in one line. A short one, in fact.

nucnorm = norm(svd(A),1);

nucnorm = norm(eig(A),1);

On a given square matrix, the two solutions will return different numbers, but will still be valid, in context of the apparent common use for this norm, that of finding a low rank matrix. (I won't bother to make the arument that this tends to induce a low rank matrix, since that is your choice to make anyway, and I don't even know if this is why you wish to compute this matrix norm.)

On a square matrix, it would appear that you might decide whether to use eig or svd in that call. Again, either seems appropriate, though svd seems generally to be faster. And since svd is neccesary for a non-square matrix, it makes sense that svd is the better choice.

MATLAB: How to find lambda from this formula

e = eig(A) returns a vector of eigenvalues of the matrix A. To get the associated eigenvectors, use [V,D] = eig(A). See the documentation for eig to interpret V and D.

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MATLAB: How to define nuclear norm in matlab

MATLAB: How to find lambda from this formula

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