Efficient algorithms for regularized Poisson Non-negative Matrix Factorization

arXiv:2404.16505v1 Announce Type: new
Abstract: We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds significant relevance in numerous Machine Learning applications, particularly within the domain of physical linear unmixing problems. A notable challenge arises from the main loss term in the Poisson NMF problem being a KL divergence, which is non-Lipschitz, rendering traditional gradient descent-based approaches inefficient. In this contribution, …

abstract algorithms applications arxiv constraints cs.lg domain factorization functions linear machine machine learning machine learning applications math.oc matrix negative regularization terms type