# Privacy-Preserving Distributed Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2403.18326 · HTML: https://mlsanity.com/paper/2403.18326/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 27 Mar 2024.

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

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Decentralized learning for wireless communications and networking](https://mlsanity.com/paper/1503.08855/) (2015)
- [Secure and Privacy-Preserving Consensus](https://mlsanity.com/paper/1707.04491/) (2017)
- [Fast and Secure Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2009.02845/) (2020)
- [A Review of Nonnegative Matrix Factorization Methods for Clustering](https://mlsanity.com/paper/1507.03194/) (2015)
- [Near-separable Non-negative Matrix Factorization with ℓ1- and Bregman Loss Functions](https://mlsanity.com/paper/1312.7167/) (2013)
- [A Case Study in Text Mining: Interpreting Twitter Data From World Cup Tweets](https://mlsanity.com/paper/1408.5427/) (2014)
- [PrivMVMF: Privacy-Preserving Multi-View Matrix Factorization for Recommender Systems](https://mlsanity.com/paper/2210.07775/) (2022)

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

- [Noise-Robust and Resource-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2409.13451/) (2024)
- [A Linearized Alternating Direction Multiplier Method for Federated Matrix Completion Problems](https://mlsanity.com/paper/2503.12733/) (2025)

## Abstract (arXiv)

Nonnegative matrix factorization (NMF) is an effective data representation tool with numerous applications in signal processing and machine learning. However, deploying NMF in a decentralized manner over ad-hoc networks introduces privacy concerns due to the conventional approach of sharing raw data among network agents. To address this, we propose a privacy-preserving algorithm for fully-distributed NMF that decomposes a distributed large data matrix into left and right matrix factors while safeguarding each agent's local data privacy. It facilitates collaborative estimation of the left matrix factor among agents and enables them to estimate their respective right factors without exposing raw data. To ensure data privacy, we secure information exchanges between neighboring agents utilizing the Paillier cryptosystem, a probabilistic asymmetric algorithm for public-key cryptography that allows computations on encrypted data without decryption. Simulation results conducted on synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm in achieving privacy-preserving distributed NMF over ad-hoc networks.