Incremental basis estimation adopting global k-means algorithm for NMF-based noise reduction

Nonnegative matrix factorization (NMF) is a data decomposition technique enabling to discover meaningful latent nonnegative components. Since, however, the objective function of NMF is non-convex, the performance of the source separation can degrade when the iterative update of the basis matrix in the training procedure is stuck to a poor local minimum. In most of the previous studies, the whole basis matrix for a specific source is iteratively updated to minimize a certain objective function with random initialization although a few approaches have been proposed for the systematic initialization of the basis matrix such as the singular value decomposition and k-means clustering. In this paper, we propose an approach to robust bases estimation in which an incremental strategy is adopted. Based on an analogy between clustering and NMF analysis, we estimate the NMF bases in a similar way to the global k-means algorithm popular in the data clustering area. Experiments on audio separation from noise showed that the proposed methods outperformed the conventional NMF technique using random initialization by about 2.04 dB and 2.34 dB in signal-to-distortion ratio when the target source was speech and violin, respectively.