NMF-based source separation utilizing prior knowledge on encoding vector

Non-negative matrix factorization (NMF) is an unsupervised technique to represents a nonnegative data matrix with a product of nonnegative basis and encoding matrices. The encoding matrix for the training phase contains information on the pattern of how each basis vector is utilized. The histogram for each row of this matrix corresponding to a specific basis turned out to be sparse, while the level of sparsity varied significantly in each basis. In this paper, the distribution of each component of an encoding vector is modeled as an independent exponential or gamma distribution, and a new objective function with the log-likelihood of the current encoding vector is proposed. Experimental results on audio source separation demonstrate that the utilization of the prior knowledge on the encoding matrix based on sparse statistical models can enhance the source separation performance.