Work

Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization

Year: 2024

Type: article

Abstract: . Simplex-structured matrix factorization (SSMF), closely related to nonnegative matrix factorization, is 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.

Source: SIAM Journal on Imaging Sciences

DOI: 10.1137/24m1650600

Authors: Maryam Abdolali, Giovanni Barbarino, Nicolas Gillis

Institutions: K. N. Toosi University of Technology, University of Mons, Istituto Nazionale di Alta Matematica Francesco Severi

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per il Calcolo Scientifico, European Research Council

Awards: G283579603, G5092193842