Maximizing Dual Simplex Volume for Interpretable Matrix Factorization

Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization that aims to find a low-rank matrix decomposition where the columns of one factor lie on the unit simplex. This paper proposes a novel approach that converts the standard minimum-volume SSMF problem in the primal space into a maximum-volume problem in the dual space, providing new insights and an efficient optimization scheme.