# Privacy-preserving Non-negative Matrix Factorization with Outliers

arXiv: https://arxiv.org/abs/2211.01451 · HTML: https://mlsanity.com/paper/2211.01451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 80 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Membership Inference Attacks on Machine Learning: A Survey](https://mlsanity.com/paper/2103.07853/) (2021)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Differential Privacy and Machine Learning: a Survey and Review](https://mlsanity.com/paper/1412.7584/) (2014)
- [Fast Differentially Private Matrix Factorization](https://mlsanity.com/paper/1505.01419/) (2015)
- [Accuracy First: Selecting a Differential Privacy Level for Accuracy-Constrained ERM](https://mlsanity.com/paper/1705.10829/) (2017)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Differentially Private Distributed Online Learning](https://mlsanity.com/paper/1505.06556/) (2015)
- [Differentially Private Distributed Convex Optimization via Functional Perturbation](https://mlsanity.com/paper/1512.00369/) (2015)
- [Online Nonnegative Matrix Factorization with Outliers](https://mlsanity.com/paper/1604.02634/) (2016)
- [Fast and Secure Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2009.02845/) (2020)

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

- [DP-CDA: An Algorithm for Enhanced Privacy Preservation in Dataset Synthesis Through Randomized Mixing](https://mlsanity.com/paper/2411.16121/) (2024)
- [Differentially Private Decentralized Dataset Synthesis Through Randomized Mixing with Correlated Noise](https://mlsanity.com/paper/2509.10385/) (2025)

## Abstract (arXiv)

Non-negative matrix factorization is a popular unsupervised machine learning algorithm for extracting meaningful features from data which are inherently non-negative. However, such data sets may often contain privacy-sensitive user data, and therefore, we may need to take necessary steps to ensure the privacy of the users while analyzing the data. In this work, we focus on developing a Non-negative matrix factorization algorithm in the privacy-preserving framework. More specifically, we propose a novel privacy-preserving algorithm for non-negative matrix factorisation capable of operating on private data, while achieving results comparable to those of the non-private algorithm. We design the framework such that one has the control to select the degree of privacy grantee based on the utility gap. We show our proposed framework's performance in six real data sets. The experimental results show that our proposed method can achieve very close performance with the non-private algorithm under some parameter regime, while ensuring strict privacy.