We provide the first positive result on nonsmooth optimization landscape of robust principal component analysis, to best our knowledge. It is object several conjectures and remains mostly uncharted territory. identify a necessary sufficient condition for absence spurious local minima in rank-one case. Our proof exploits subdifferential regularity objective function order eliminate existence qua...

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as non-convex optimization problem, making it sensitive the initialization of variables. Inspired by ensemble clustering that aims seek better result from set results, we propose self-supervised (S <sup xmlns:mml="http://www.w3.org/1998/Math/...

We formulate an equivalence between the 2-dim $\ensuremath{\sigma}$-model spectrum expanded on a nontrivial massive vacuum and classical particle Hamiltonian with variable mass potential. By considering methods of analytic Galoisian nonintegrability appropriate geodesics system we algebraically constrain masses at fixed time, such that integrability is allowed. Through our equivalence, this exp...

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‐b...