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.

翻译：非负矩阵分解（NMF）是一种有效的数据表示工具，在信号处理和机器学习领域具有广泛应用。然而，在自组织网络中采用分散方式部署NMF时，由于传统方法需要在网络智能体间共享原始数据，会引发隐私问题。为解决此问题，我们提出一种面向全分布式NMF的隐私保护算法，该算法在保护每个智能体本地数据隐私的同时，将分布式大矩阵分解为左、右矩阵因子。该算法能促进智能体间对左矩阵因子的协同估计，并使其在无需暴露原始数据的情况下分别估计各自的右矩阵因子。为确保数据隐私，我们利用Paillier密码系统（一种基于概率非对称算法的公钥密码机制，支持对加密数据进行运算而无需解密）来保护相邻智能体间的信息交换。在合成数据集和真实数据集上的仿真结果证明了所提算法在自组织网络中实现隐私保护分布式NMF的有效性。