Identifiability of Nonnegative Tensor Decompositions via Positive Scattering

The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.

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