Instantaneous Versus Convolutive Non-Negative Matrix Factorization

Abstract

Non-negative matrix factorization (NMF) is an emerging technique for data analysis and machine learning, which aims to find low-rank representations for non-negative data. Early works in NMF are mainly based on the instantaneous model, i.e. using a single basis matrix to represent the data. Recent works have shown that the instantaneous model may not be satisfactory for many audio application tasks. The convolutive NMF model, which has an advantage of revealing the temporal structure possessed by many signals, has been proposed. This chapter intends to provide a brief overview of the models and algorithms for both the instantaneous and the convolutive NMF, with a focus on the theoretical analysis and performance evaluation of the convolutive NMF algorithms, and their applications to audio pattern separation problems.