Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization

arXiv:2403.20197v1 Announce Type: cross
Abstract: Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization, a fundamental interpretable data analysis model, and has applications in hyperspectral unmixing and topic modeling. To obtain identifiable solutions, a standard approach is to find minimum-volume solutions. By taking advantage of the duality/polarity concept for polytopes, we convert minimum-volume SSMF in the primal space to a maximum-volume problem in the dual space. We first prove the identifiability of this maximum-volume dual problem. Then, we …

abstract analysis applications arxiv concept cs.ir cs.lg cs.na data data analysis eess.sp factorization math.na matrix modeling solutions standard stat.ml topic modeling type