Nonnegative approximations of nonnegative tensors

Abstract : We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naive Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative Parafac, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Bregman divergences.
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Submitted on : Sunday, August 16, 2009 - 8:19:37 PM
Last modification on : Monday, November 5, 2018 - 3:52:01 PM
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Lek-Heng Lim, Pierre Comon. Nonnegative approximations of nonnegative tensors. Journal of Chemometrics, Wiley, 2009, 23, pp.432-441. ⟨10.1002/cem.1244⟩. ⟨hal-00410056⟩

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