Details

Autor(en) / Beteiligte

• Finesso, Lorenzo
• Spreij, Peter

Titel

Nonnegative matrix factorization and I-divergence alternating minimization

Ist Teil von

• Linear algebra and its applications, 2006-07, Vol.416 (2), p.270-287

Ort / Verlag

New York, NY: Elsevier Inc

Erscheinungsjahr

2006

Link zum Volltext

Quelle

Access via ScienceDirect (Elsevier)

Beschreibungen/Notizen

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