I know that the covariance of a matrix can be computed directly by using the data matrix $$Cov(Data) = X'X $$. And also can be computed via the the singular values S and V diagonal matrix of SVD that is $$Cov(Data) = V * S^2 * V' $$. The output of this matrix is a square matrix of size n; where n represents the feature dimensions of the input data.
I want to know what is the meaning of the multiplying singular values S and the U diagonal matrix that is $$ U * S * U'$$. The output of this matrix is again a square matrix of size m; where m represents the number of samples.
I am reading a code which does exactly this second calculation and the result is assigned to a variable called similarity. Is this calculation is know as some kind of distance metric between different data points ?
I would really appreciate if someone shed light on this subject.
Best Regards