Temporal Extensions of Nonnegative Matrix Factorization

Book chapter, 2018

Temporal continuity is one of the most important features of time series data. In this chapter, we present several ways of modeling time dependencies in nonnegative matrix factorization (NMF). The dependencies between consecutive frames of the spectrogram can be imposed either on the basis matrix or on the activations. The former case is known as the convolutive NMF: in this case, the repeating patterns within data are represented with multidimensional bases instead of vectors. The other case consists in imposing temporal structure on the activations, in line with traditional dynamic models. Most models considered in the NMF literature can be cast as special cases of a unifying state-space model that will be discussed. Special cases include continuous and discrete models. We provide quantitative and qualitative comparisons of the proposed methods.