核心概念
This work presents efficient algorithms for solving the regularized Poisson Non-negative Matrix Factorization (NMF) problem with linear constraints.
摘要
The key highlights and insights of this content are:
The authors consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF), which encompasses various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem is relevant in numerous Machine Learning applications, particularly within the domain of physical linear unmixing problems.
A notable challenge in the Poisson NMF problem is that the main loss term, the KL divergence, is non-Lipschitz, rendering traditional gradient descent-based approaches inefficient. The authors explore the utilization of Block Successive Upper Minimization (BSUM) to overcome this challenge.
The authors build appropriate majorizing functions 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: a Multiplicative Update (MU) algorithm and a Quadratic Update (QU) algorithm.
The authors conduct numerical simulations to showcase the effectiveness of their approach, demonstrating the advantages of their algorithms compared to traditional methods.