Efficient algorithms for regularized Poisson Non-negative Matrix Factorization
This addresses a computational bottleneck in physical linear unmixing problems in machine learning, but it is incremental as it builds on existing BSUM methods.
The authors tackled the challenge of regularized Poisson Non-negative Matrix Factorization, where the KL divergence loss is non-Lipschitz, by developing two novel algorithms using Block Successive Upper Minimization with majorizing functions for Lipschitz and relatively smooth regularizations and linear constraints, and demonstrated effectiveness through numerical simulations.
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, we explore the utilization of Block Successive Upper Minimization (BSUM) to overcome this challenge. We build approriate majorizing function for Lipschitz and relatively smooth functions, and show how to introduce linear constraints into the problem. This results in the development of two novel algorithms for regularized Poisson NMF. We conduct numerical simulations to showcase the effectiveness of our approach.