FastMNMF: Joint Diagonalization Based Accelerated Algorithms for Multichannel Nonnegative Matrix Factorization

A multichannel extension of nonnegative matrix factorization (NMF) for audio/music data, called multichannel NMF (MNMF), has been proposed by Sawada et al ["Multichannel extensions of non-negative matrix factorization with complex-valued data IEEE Trans. ASLP, vol. 21, no. 5, pp. 971-982, May 2013]. However, conventional MNMF algorithms have a major drawback of a heavy computational load due to numerous matrix operations, such as matrix inversions and matrix multiplications. Here we propose FastMNMF, accelerated algorithms for the MNMF based on joint diagonalization of matrices. It is well known that, for diagonal matrices, matrix operations reduce to mere scalar operations on diagonal entries. Because of this property, the joint diagonalization results in a significantly reduced computational load compared to conventional MNMF algorithms. This makes the proposed FastMNMF even applicable to a situation with alarge database or restricted computational resources.