Privacy-Preserving Distributed Nonnegative Matrix Factorization

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.