A Distributed HALS Algorithm for Euclidean Distance-Based Nonnegative Matrix Factorization

Abstract

This paper proposes a distributed algorithm for multiple agents to perform the Nonnegative Matrix Factorization (NMF) based on the Euclidean distance. The matrix to be factorized is partitioned into multiple blocks, and each block is assigned to one of the agents forming a two-dimensional grid network. Each agent handles a small number of entries of the factor matrices corresponding to the assigned block, and updates their values by using information coming from the neighbors. It is shown that the proposed algorithm simulates the hierarchical alternating least squares method, which is well known as a fast algorithm for NMF based on the Euclidean distance, by making use of a finite-time distributed consensus algorithm.