Partial Identifiability for Nonnegative Matrix Factorization

Given a nonnegative matrix factorization, , and factorization rank, exact (exact NMF) decomposes as the product of two matrices, with columns, such . A central research topic in literature is conditions under which decomposition unique/identifiable up to trivial ambiguities. In this paper, we focus on partial identifiability, that is, uniqueness subset columns We start our investigations data‐based (DBU) theorem from chemometrics literature. The DBU analyzes all feasible solutions NMF relies sparsity provide mathematically rigorous recently published restricted version theorem, relying only simple algebraic conditions: it applies particular solution (as opposed solutions) allows us guarantee single column or Second, based geometric interpretation obtain new identifiability result. This also leads another result case Third, show how results can be used sequentially more illustrate these several examples, including one