How do you estimate the mean in a Non-Negative Matrix Factorization framework?
It is obvious and well known how to estimate the covariance matrix, how ever I also need the estimated mean. I'm assuming there is a way to estimate the mean via regression as there is with similar algorithm's such as PCA and this should already be derived for Non-Negative Matrix Factorization. I just can't find it in the literature and common frameworks do not provide this and only return the matrix factorization (MatLab, R ,Python exc...).
Using the terminology from MatLab.
A represents an
NxM Matrix (Could be 1 + Returns or Volumes or generally any positive matrix). One can compute
nnmf(A) to get
[W, H, D] where
W*H is a lower-rank approximation to
Is this as simple as computing the direct mean and covariance of
W*H or am I missing something?