  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.
