# Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization

arXiv: https://arxiv.org/abs/2608.28799 · HTML: https://mlsanity.com/paper/2608.28799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [A Scale Invariant Approach for Sparse Signal Recovery](https://mlsanity.com/paper/1812.08852/) (2018)
- [Limited-angle CT reconstruction via the L1/L2 minimization](https://mlsanity.com/paper/2006.00601/) (2020)
- [A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary](https://mlsanity.com/paper/1610.01349/) (2016)
- [Memory-Efficient Convex Optimization for Self-Dictionary Separable Nonnegative Matrix Factorization: A Frank-Wolfe Approach](https://mlsanity.com/paper/2109.11135/) (2021)
- [Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recovery](https://mlsanity.com/paper/2405.08275/) (2024)
- [An Efficient ADMM Method for Ratio-Type Nonconvex and Nonsmooth Minimization in Sparse Recovery](https://mlsanity.com/paper/2509.21969/) (2025)

## Abstract (arXiv)

Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its ability to produce part-based and interpretable decompositions. In particular, SNMF is closely related to graph clustering and community detection. To enhance sparsity and identifiability of the learned factors, we propose an ℓ1p/ℓ2-regularized SNMF model based on a powered ratio-of-norms regularizer. The resulting formulation is nonconvex and nonsmooth, which poses significant challenges for optimization. To address this, we develop efficient algorithms based on the difference-of-convex function algorithm (DCA) and the alternating direction method of multipliers (ADMM). The proposed methods decompose the original problem into tractable subproblems, leveraging closed-form proximal operators associated with the powered norm terms. We establish descent and limiting criticality properties for the DCA scheme and convergence under standard assumptions for the ADMM scheme. Extensive numerical experiments on synthetic datasets and hand gesture classification tasks demonstrate that the proposed approach achieves competitive or improved performance in anchor identification and classification accuracy compared with existing SNMF methods, while maintaining competitive computational efficiency.