HALS-based algorithm for affine non-negative matrix factorization

Non-negative matrix factorization (NMF) learns to approximate a non-negative matrix by the product of two lower-rank non-negative matrices. Since NMF usually learns sparse representation,it has been widely used in pattern recognition and data mining. However, NMF cannot deal with the datasets that contain offsets. To remedy this problem, Laurberg and Hansen proposed affine NMF (ANMF) by jointly learning the offset vector, but the proposed multiplicative update rule neither guarantees non-negativity constraints over factor matrices nor converges sufficiently rapid. In this paper, we adopt the well-known hierarchical alternating least squares (HALS) algorithm to solve ANMF. Since the update of offset vector is in the same frame of updates of factor matrices, HALS is quite suitable for solving ANMF and the experimental results on simulated datasets validate its efficiency.