# Graph Regularized NMF with L20-norm for Unsupervised Feature Learning

arXiv: https://arxiv.org/abs/2403.10910 · HTML: https://mlsanity.com/paper/2403.10910/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 16 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [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)
- [Text Mining using Nonnegative Matrix Factorization and Latent Semantic Analysis](https://mlsanity.com/paper/1911.04705/) (2019)
- [An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2308.12126/) (2023)

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

- [Real-time Multi-instrument Autonomous Discovery of Novel Phase-change Memory Materials](https://mlsanity.com/paper/2605.18033/) (2026)
- [scASDC: Attention Enhanced Structural Deep Clustering for Single-cell RNA-seq Data](https://mlsanity.com/paper/2408.05258/) (2024)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization constraints. GNMF has demonstrated exceptional performance in clustering and dimensionality reduction, effectively discovering inherent low-dimensional structures embedded within high-dimensional spaces. However, the sensitivity of GNMF to noise limits its stability and robustness in practical applications. In order to enhance feature sparsity and mitigate the impact of noise while mining row sparsity patterns in the data for effective feature selection, we introduce the ℓ2,0-norm constraint as the sparsity constraints for GNMF. We propose an unsupervised feature learning framework based on GNMF_ℓ20 and devise an algorithm based on PALM and its accelerated version to address this problem. Additionally, we establish the convergence of the proposed algorithms and validate the efficacy and superiority of our approach through experiments conducted on both simulated and real image data.