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• W2012642013 abstract "In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V in R_+^{mtimes n}$ find, for assigned $k$, nonnegative matrices $WinR_+^{mtimes k}$ and $HinR_+^{ktimes n}$ such that $V=WH$. Exact, non trivial, 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 `a la Csisz'ar-Tusn'ady 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." @default.
• W2012642013 created "2016-06-24" @default.
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• W2012642013 date "2006-07-01" @default.
• W2012642013 modified "2023-09-28" @default.
• W2012642013 title "Nonnegative matrix factorization and I-divergence alternating minimization" @default.
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• W2012642013 doi "https://doi.org/10.1016/j.laa.2005.11.012" @default.
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