Identifiability of Nonnegative Tensor Decompositions via Positive Scattering

Classical criteria for tensor decomposition uniqueness, such as Kruskal's theorem, rely primarily on linear-algebraic dimension bounds, largely bypassing the structural rigidity enforced by entrywise nonnegativity. This paper introduces a positive scattering term that leverages non-cancellation and support constraints to certify identifiability. By establishing a positive splitting inequality, the authors prove two distinct component thresholds (2|S|-2 for rank minimality and 2|S|-1 for uniqueness) reducible to graph connectivity checks, successfully certifying sparse nonnegative tensor decompositions where generalized Kruskal conditions fail.