Distributed HALS Algorithm for NMF based on Simple Average Consensus Algorithm

Abstract

Nonnegative Matrix Factorization (NMF) is an efficient dimensionality reduction method for nonnegative data. Recently, a distributed algorithm has been proposed for multiple agents in a network to execute the hierarchical alternating least squares algorithm, which is well known as a fast computation method for NMF. However, the average consensus algorithm used there requires each agent to store the entire history of the values of its variables until the complete average consensus is reached, which increases the memory usage and computational cost. In this paper, we propose to replace the complicated average consensus algorithm with a simple one, and show through simulations that this replacement does not degrade the quality of the result if the values of the hyper-parameters are properly chosen.