Instantaneous vs. Convolutive Non-Negative Matrix Factorization: Models, Algorithms and Applications to Audio Pattern Separation

Since the seminal paper published in 1999 by Lee and Seung, non-negative matrix factorization (NMF) has attracted tremendous research interests over the last decade. The earliest work in NMF is perhaps by (Paatero, 1997) and is then made popular by Lee and Seung due to their elegant multiplicative algorithms (Lee & Seung, 1999, Lee & Seung, 2001). The aim of NMF is to look for latent structures or features within a dataset, through the representation of a non-negative data matrix by a product of low rank matrices. It was found in (Lee & Seung, 1999) that NMF results in a “parts” based representation, due to the nonnegative constraint. This is because only additive operations are allowed in the learning process. Although later works in NMF may have mathematical operations that can lead to negative elements within the low-rank matrices, their abStract