Incorporate another dimension to non-negative matrix factorization (NMF)?

1. Why is NMF non-negative?
2. How does non-negative matrix factorization work?
3. What distribution is used to model the elements of the matrix in non-negative matrix factorization?
4. What is the main advantage of NMF non-negative matrix factorization over SVD as a dimension reduction technique?

Why is NMF non-negative?

Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements.

How does non-negative matrix factorization work?

Non-Negative Matrix Factorization uses techniques from multivariate analysis and linear algebra. It decomposes the data as a matrix M into the product of two lower ranking matrices W and H. The sub-matrix W contains the NMF basis; the sub-matrix H contains the associated coefficients (weights).

What distribution is used to model the elements of the matrix in non-negative matrix factorization?

poisson distribution - Nonnegative Matrix Factorization as Maximum Likelihood - Cross Validated.

What is the main advantage of NMF non-negative matrix factorization over SVD as a dimension reduction technique?

Therefore, the main difference of NMF from the other dimension reduction methods (e.g., SVD) is that NMF allows only non-subtractive combinations of nonnegative components. This nonnegativity constraint eventually leads to the parts-based representation of NMF.