Block-Iterative Algorithms for Non-negative Matrix Approximation

In this paper we present new algorithms for non-negative matrix approximation (NMA), commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee & Seung [12] for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem. For the latter problem, our results are especially interesting because it seems to have witnessed much lesser algorithmic progress as compared to the Frobenius norm NMA problem. Our algorithms are based on a particular block-iterative acceleration technique for EM, which preserves the multiplicative nature of the updates and also ensures monotonicity. Furthermore, our algorithms also naturally apply to the Bregman-divergence NMA algorithms of [6]. Experimentally,we show that our algorithms outperform the traditional Lee/Seung approach most of the time.