Nonnegative approximations of nonnegative tensors

Details Nonnegative approximations of nonnegative tensors Nonnegative approximations of nonnegative tensors

2009-03-26

arxiv.org/abs/0903.4530v2

Computer Science

Numerical Analysis

14 pages

Scientific paper

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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