Nonnegative matrix factorization and I-divergence alternating minimization☆

摘要: Abstract In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix V ∈ R + m × n find, for assigned k, matrices W k and H such that V = WH. Exact, nontrivial, factorizations do not always exist, hence it is interesting to pose approximate NMF problem. The criterion which commonly employed I-divergence between matrices. problem becomes of finding, factorization WH closest in I-divergence. An iterative algorithm, EM like, construction best pair (W, H) has been proposed literature. interpret algorithm as alternating minimization procedure a la Csiszar–Tusnady investigate some its stability properties. widespreading data analysis method applications positivity constraint relevant. There are other methods impose form nonnegativity: discuss here connections Archetypal Analysis.