# Towards a Fairer Non-negative Matrix Factorization

arXiv: https://arxiv.org/abs/2411.09847 · HTML: https://mlsanity.com/paper/2411.09847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 14 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [A Survey on the Fairness of Recommender Systems](https://mlsanity.com/paper/2206.03761/) (2022)
- [Scalable Fair Clustering](https://mlsanity.com/paper/1902.03519/) (2019)
- [User-oriented Fairness in Recommendation](https://mlsanity.com/paper/2104.10671/) (2021)
- [Proportionally Fair Clustering](https://mlsanity.com/paper/1905.03674/) (2019)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Individual Fairness for k-Clustering](https://mlsanity.com/paper/2002.06742/) (2020)
- [Learning Multimorbidity Patterns from Electronic Health Records Using Non-negative Matrix Factorisation](https://mlsanity.com/paper/1907.08577/) (2019)
- [Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization](https://mlsanity.com/paper/1901.10757/) (2019)
- [Identifiable Phenotyping using Constrained Non-Negative Matrix Factorization](https://mlsanity.com/paper/1608.00704/) (2016)
- [Fair Matrix Factorisation for Large-Scale Recommender Systems](https://mlsanity.com/paper/2209.04394/) (2022)
- [Feature Selection on Lyme Disease Patient Survey Data](https://mlsanity.com/paper/2009.09087/) (2020)

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

- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)
- [Improving Group Fairness in Tensor Completion via Imbalance Mitigating Entity Augmentation](https://mlsanity.com/paper/2507.20542/) (2025)

## Abstract (arXiv)

There has been a recent critical need to study fairness and bias in machine learning (ML) algorithms. Since there is clearly no one-size-fits-all solution to fairness, ML methods should be developed alongside bias mitigation strategies that are practical and approachable to the practitioner. Motivated by recent work on ``fair" PCA, here we consider the more challenging method of non-negative matrix factorization (NMF) as both a showcasing example and a method that is important in its own right for both topic modeling tasks and feature extraction for other ML tasks. We demonstrate that a modification of the objective function, by using a min-max formulation, may textitsometimes be able to offer an improvement in fairness for groups in the population. We derive two methods for the objective minimization, a multiplicative update rule as well as an alternating minimization scheme, and discuss implementation practicalities. We include a suite of synthetic and real experiments that show how the method may improve fairness while also highlighting the important fact that this may sometime increase error for some individuals and fairness is not a rigid definition and method choice should strongly depend on the application at hand.