Using population based algorithms for initializing nonnegative matrix factorization

Abstract

The nonnegative matrix factorization (NMF) is a bound-constrained low-rank approximation technique for nonnegative multivariate data. NMF has been studied extensively over the last years, but an important aspect which only has received little attention so far is a proper initialization of the NMF factors in order to achieve a faster error reduction. Since the NMF objective function is usually non-differentiable, discontinuous, and may possess many local minima, heuristic search algorithms are a promising choice as initialization enhancers for NMF. In this paper we investigate the application of five population based algorithms (genetic algorithms, particle swarm optimization, fish school search, differential evolution, and fireworks algorithm) as new initialization variants for NMF. Experimental evaluation shows that some of them are well suited as initialization enhancers and can reduce the number of NMF iterations needed to achieve a given accuracy. Moreover, we compare the general applicability of these five optimization algorithms for continuous optimization problems, such as the NMF objective function. © 2011 Springer-Verlag.