mlsanityData to 14 Oct 2026

Efficient algorithms for regularized Poisson Non-negative Matrix Factorization

arXiv 2404.16505 ↗First posted 25 Apr 2024cs.LG math.OCcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 14 of its 60 references that are in the map. First posted on arXiv 25 Apr 2024.

Builds on

14 of 60 references.

References · 14

  1. 2017How to Escape Saddle Points Efficientlycited by 285
  2. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  3. 2014Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learningcited by 35
  4. 2019First-order methods almost always avoid saddle points: the case of vanishing step-sizescited by 35
  5. 2014The Why and How of Nonnegative Matrix Factorizationcited by 34
  6. 2014Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problemscited by 25
  7. 2018A Newton-CG Algorithm with Complexity Guarantees for Smooth Unconstrained Optimizationcited by 23
  8. 2018Accelerated Bregman Proximal Gradient Methods for Relatively Smooth Convex Optimizationcited by 20
  9. 2020Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergencecited by 17
  10. 2017Complexity analysis of second-order line-search algorithms for smooth nonconvex optimizationcited by 16
  11. 2013Scalable Recommendation with Poisson Factorizationcited by 8
  12. 2014Primal-Dual Algorithms for Non-negative Matrix Factorization with the Kullback-Leibler Divergencecited by 4
2 more
  1. 2019Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problemscited by 3
  2. 2016Fast and Simple Optimization for Poisson Likelihood Modelscited by 2

Built on by

Not cited yet.