# Structured Sparse Non-negative Matrix Factorization with L20-Norm for scRNA-seq Data Analysis

arXiv: https://arxiv.org/abs/2104.13171 · HTML: https://mlsanity.com/paper/2104.13171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 27 Apr 2021.

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

- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization](https://mlsanity.com/paper/1705.04925/) (2017)
- [On the Convergence of Learning-based Iterative Methods for Nonconvex Inverse Problems](https://mlsanity.com/paper/1808.05331/) (2018)
- [Clustering by Orthogonal NMF Model and Non-Convex Penalty Optimization](https://mlsanity.com/paper/1906.00570/) (2019)
- [Sparse K-Means with ℓ∞/ℓ0 Penalty for High-Dimensional Data Clustering](https://mlsanity.com/paper/1403.7890/) (2014)

## Built on by (most cited first, 2 of 2)

- [Precise Facial Landmark Detection by Reference Heatmap Transformer](https://mlsanity.com/paper/2303.07840/) (2023)
- [scASDC: Attention Enhanced Structural Deep Clustering for Single-cell RNA-seq Data](https://mlsanity.com/paper/2408.05258/) (2024)

## Abstract (arXiv)

Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data without effective feature selection. In this paper, we first introduce a row-sparse NMF with ℓ2,0-norm constraint (NMF_ℓ20), where the basis matrix W is constrained by the ℓ2,0-norm, such that W has a row-sparsity pattern with feature selection. It is a challenge to solve the model, because the ℓ2,0-norm is non-convex and non-smooth. Fortunately, we prove that the ℓ2,0-norm satisfies the Kurdyka-Lojasiewicz property. Based on the finding, we present a proximal alternating linearized minimization algorithm and its monotone accelerated version to solve the NMF_ℓ20 model. In addition, we also present a orthogonal NMF with ℓ2,0-norm constraint (ONMF_ℓ20) to enhance the clustering performance by using a non-negative orthogonal constraint. We propose an efficient algorithm to solve ONMF_ℓ20 by transforming it into a series of constrained and penalized matrix factorization problems. The results on numerical and scRNA-seq datasets demonstrate the efficiency of our methods in comparison with existing methods.