# Entropy Minimizing Matrix Factorization

arXiv: https://arxiv.org/abs/2103.13487 · HTML: https://mlsanity.com/paper/2103.13487/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 81 references that are in the map.
- First posted on arXiv 24 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Fast Adaptively Weighted Matrix Factorization for Recommendation with Implicit Feedback](https://mlsanity.com/paper/2003.01892/) (2020)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Fast Matrix Factorization with Non-Uniform Weights on Missing Data](https://mlsanity.com/paper/1811.04411/) (2018)
- [Truncated Cauchy Non-negative Matrix Factorization](https://mlsanity.com/paper/1906.00495/) (2019)
- [Multi-View Multiple Clusterings using Deep Matrix Factorization](https://mlsanity.com/paper/1911.11396/) (2019)
- [Generalized Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1905.12995/) (2019)
- [L'evy NMF for robust nonnegative source separation](https://mlsanity.com/paper/1608.01844/) (2016)
- [Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation](https://mlsanity.com/paper/1707.05147/) (2017)
- [Complex ISNMF: a Phase-Aware Model for Monaural Audio Source Separation](https://mlsanity.com/paper/1802.03156/) (2018)

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

- [Concept Factorization via Self-Representation and Adaptive Graph Structure Learning](https://mlsanity.com/paper/2505.03390/) (2025)
- [Multi-Task Curriculum Graph Contrastive Learning with Clustering Entropy Guidance](https://mlsanity.com/paper/2408.12071/) (2024)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal centroids by minimizing the sum of the approximation errors. However, the outliers deviating from the normal data distribution may have large residues, and then dominate the objective value seriously. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization, which minimizes the entropy of the residue distribution and allows a few samples to have large approximation errors. In this way, the outliers do not affect the approximation of the normal samples. The multiplicative updating rules for EMMF are also designed, and the convergence is proved both theoretically and experimentally. In addition, a Graph regularized version of EMMF (G-EMMF) is also presented to deal with the complex data structure. Clustering results on various synthetic and real-world datasets demonstrate the reasonableness of the proposed models, and the effectiveness is also verified through the comparison with the state-of-the-arts.