Squared Euclidean Distance Based Convolutive Non-Negative Matrix Factorization with Multiplicative Learning Rules For Audio Pattern Separation

A novel algorithm for convolutive non-negative matrix factorization (NMF) with multiplicative rules is presented in this paper. In contrast to the standard NMF, the low rank approximation is represented by a convolutive model which has an advantage of revealing the temporal structure possessed by many realistic signals. The convolutive basis decomposition is obtained by the minimization of the conventional squared Euclidean distance, rather than the Kullback-Leibler divergence. The algorithm is applied to the audio pattern separation problem in the magnitude spectrum domain. Numerical experiments suggest that the proposed algorithm has both less computational loads and better separation performance for auditory pattern extraction, as compared with an existing method developed by Smaragdis.