Deep alternating non-negative matrix factorisation

Abstract

Non-negative matrix factorisation (NMF) is a promising data-mining technique for non-negative data. NMF achieves feature extraction by factorising the original data matrix into a basis matrix and coding matrix both with non-negative entries. Recently, multi-layer or deep NMF has been studied because of its ability to extract deep representative features which can help profoundly understand the original data. The existing deep NMF approaches are implemented by cascading the factorisation of the coding matrix at each layer. This paper proposes a novel scheme, in which the factorisations of the basis and coding matrices are alternated along layers. Based on this scheme, several deep NMF models to address various data scenarios are developed. Extensive experimental results on several machine learning tasks, including collaborative filtering, image inpainting, and community detection, show that the proposed alternating deep factorisation algorithms perform significantly better than existing state-of-the-art algorithms in most instances of these tasks.