Nonnegative matrix factorization: When data is not nonnegative

In this paper, we present a new variations of the popular nonnegative matrix factorization (NMF) approach to extend it to the data with negative values. When a NMF problem is formulated as X ≈ HW, we try to develop a new method that only allows W to contain nonnegative values, but allows both X and H to have both nonnegative and negative values. In this way, the original NMF is extended to be used for real value data matrix instead restricted to only negative value data matrix. To this end, we develops novel method to factorize the real value data matrix. The method is evaluated experimentally and the results showed its effectiveness.