Algorithms for Nonnegative Matrix Factorization with the Kullback–Leibler Divergence

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between input and low-rank approximation, Kullback-Leibler (KL) divergence one of most widely used objective function NMF. It corresponds maximum likehood estimator when underlying statistics observed sample follows Poisson distribution, KL NMF particularly meaningful count sets, such as documents or images. this paper, we first collect important properties that are essential study convergence algorithms. Second, together with reviewing existing algorithms solving NMF, propose three new guarantee non-increasingness function. We also provide global our proposed Finally, conduct extensive numerical experiments comprehensive picture performances