Dual Simplex Volume Maximization for Simplex-Structured Matrix
  Factorization
Maryam Abdolali Giovanni Barbarino Nicolas Gillis
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 use this dual formulation to provide a novel
optimization approach which bridges the gap between two existing families of
algorithms for SSMF, namely volume minimization and facet identification.
Numerical experiments show that the proposed approach performs favorably
compared to the state-of-the-art SSMF algorithms.