FWA Application on Non-negative Matrix Factorization

Abstract

This chapter presents the use of swarm intelligence algorithms for non-negative matrix factorization (NMF) Janecek and Tan (2011) International Journal of Swarm Intelligence Research (IJSIR) 2(4):12–34, [1]. The NMF is a special low-rank approximation which allows for an additive parts-based and interpretable representation of the data. Here, we present our efforts to improve the convergence and approximation quality of NMF using five different meta-heuristics based on swarm intelligence. Several properties of the NMF objective function motivate the utilization of meta-heuristics: this function is non-convex, discontinuous, and may possess many local minima. The proposed optimization strategies are twofold: On one hand, we present a new initialization strategy for NMF in order to initialize the NMF factors prior to the factorization; on the other hand, we present an iterative update strategy which improves the accuracy per runtime for the multiplicative update NMF algorithm.