Structure selection for convolutive non-negative matrix factorization using normalized maximum likelihood coding

Abstract

Convolutive non-negative matrix factorization (CNMF) is a promising method for extracting features from sequential multivariate data. Conventional algorithms for CNMF require that the structure, or the number of bases for expressing the data, be specified in advance. We are concerned with the issue of how we can select the best structure of CNMF from given data. We first introduce a framework of probabilistic modeling of CNMF and reduce this issue to statistical model selection. The problem is here that conventional model selection criteria such as AIC, BIC, MDL cannot straightforwardly be applied since the probabilistic model for CNMF is irregular in the sense that parameters are not uniquely identifiable. We overcome this problem to propose a novel criterion for best structure selection for CNMF. The key idea is to apply the technique of latent variable completion in combination with normalized maximum likelihood coding criterion under the minimum description length principle. We empirically demonstrate the effectiveness of our method using artificial and real data sets.