Recursive least squares-based online nonnegative matrix factorization (RLS-ONMF), an NMF algorithm based on the RLS method, was developed to solve the NMF problem online. However, this method suffers from a partial-data problem. In this study, the partial-data problem is resolved by developing an improved online NMF algorithm using RLS and a sparsity constraint. The proposed method, RLS-based online sparse NMF (RLS-OSNMF), consists of two steps; an estimation step that optimizes the Euclidean NMF cost function, and a shaping step that satisfies the sparsity constraint. The proposed algorithm was evaluated with recorded speech and music data and with the RWC music database. The results show that the proposed algorithm performs better than conventional RLS-ONMF, especially during the adaptation process.

In this paper, an on-line nonnegative matrix factorization (NMF) algorithm for acoustic signal processing systems is developed based on the recursive least squares (RLS) method. In order to develop the on-line NMF algorithm, we reformulate the NMF problem into multiple least squares (LS) normal equations, and solve the reformulated problems using RLS methods. In addition, we eliminate the irrelevant calculations based on the NMF model. The proposed algorithm has been evaluated with a well-known dataset used for NMF performance evaluation and with real acoustic signals; the results show that the proposed algorithm performs better than the conventional algorithm in on-line applications.