Nonnegative Matrix and Tensor Factorization [Lecture Notes]

In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not necessary the best approaches for NMF, especially if data representations are not very redundant or sparse. 2) Much better performance can be achieved using the FP-ALS (especially for large-scale problems), IPC, and QN methods. 3) To achieve high performance it is quite important to use the multilayer structure with multistart initialization conditions. 4) To estimate physically meaningful nonnegative components it is often necessary to use some a priori knowledge and impose additional constraints or regularization terms (to control sparsity, boundness, continuity or smoothness of the estimated nonnegative components).