About Matrix Factorization's Result Matrices

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About Matrix Factorization's Result Matrices

seyfullahd
Hello again :)

I wanna ask a question about matrix factorizations just to be sure. In SVD method a matrix is reduced to U x E x tranpose of V matrices where the U is baseMatrix and the V itself is the coefficientMatrix. First, this is true, right?

And the second, are the other factorization methods's results matrices after their factorization process conceptually alike to SVD method. I mean the resulting baseMatrix and coefficientMatrix are alike to SVD's results, right? for instance alike as sizes and conceptual meaning?

Thanks in advance,

Seyfullah
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Re: About Matrix Factorization's Result Matrices

seyfullahd
I found a difference among them by the way :)

LocalNonnegativeMatrixFactorization and NonnegativeMatrixFactorizationKL methods' base matrices (U matrix) are column-length-normalized but the others' are not.

Seyfullah
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Re: About Matrix Factorization's Result Matrices

Stanislaw Osinski-3

LocalNonnegativeMatrixFactorization and NonnegativeMatrixFactorizationKL
methods' base matrices (U matrix) are column-length-normalized but the
others' are not.

That is correct (looking at the implementation). Why or if the normalization is required, I don't remember. I'd have to get back to the tens of factorization papers I read 10 years ago :-)

S.


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