# Block Majorization Minimization with Extrapolation and Application to β-NMF

arXiv: https://arxiv.org/abs/2401.06646 · HTML: https://mlsanity.com/paper/2401.06646/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 12 Jan 2024.

## Builds on (most cited first, 16 of 16)

- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Survey](https://mlsanity.com/paper/1708.05125/) (2017)
- [iPiano: Inertial Proximal Algorithm for Non-Convex Optimization](https://mlsanity.com/paper/1404.4805/) (2014)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2010.01935/) (2020)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF](https://mlsanity.com/paper/1907.02404/) (2019)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano](https://mlsanity.com/paper/1602.07283/) (2016)
- [Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation](https://mlsanity.com/paper/1805.06604/) (2018)
- [Block majorization-minimization with diminishing radius for constrained nonsmooth nonconvex optimization](https://mlsanity.com/paper/2012.03503/) (2020)
- [Multiplicative Updates for NMF with β-Divergences under Disjoint Equality Constraints](https://mlsanity.com/paper/2010.16223/) (2020)
- [Joint Majorization-Minimization for Nonnegative Matrix Factorization with the β-divergence](https://mlsanity.com/paper/2106.15214/) (2021)
- [Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs](https://mlsanity.com/paper/1705.07229/) (2017)
- [Majorization-minimization for Sparse Nonnegative Matrix Factorization with the β-divergence](https://mlsanity.com/paper/2207.06316/) (2022)
- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)

## Built on by (most cited first, 1 of 1)

- [An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2607.13919/) (2026)

## Abstract (arXiv)

We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that block majorization minimization can be reformulated as a block mirror descent method, with the Bregman divergence adaptively updated at each iteration, we establish subsequential convergence for BMMe. We use this method to design efficient algorithms to tackle nonnegative matrix factorization problems with the β-divergences (β-NMF) for β∈ [1,2]. These algorithms, which are multiplicative updates with extrapolation, benefit from our novel results that offer convergence guarantees. We also empirically illustrate the significant acceleration of BMMe for β-NMF through extensive experiments.