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Imaging Sci."],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>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.\u00a0To 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.\u00a0Then, 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.<\/jats:p>","DOI":"10.1137\/24m1650600","type":"journal-article","created":{"date-parts":[[2024,12,10]],"date-time":"2024-12-10T04:01:49Z","timestamp":1733803309000},"page":"2362-2391","source":"Crossref","is-referenced-by-count":3,"title":["Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization"],"prefix":"10.1137","volume":"17","author":[{"given":"Maryam","family":"Abdolali","sequence":"first","affiliation":[{"name":"K. N. Toosi University (KNTU), Tehran, Iran."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0504-7361","authenticated-orcid":true,"given":"Giovanni","family":"Barbarino","sequence":"additional","affiliation":[{"name":"University of Mons, Mons, Belgium.\u00a0GB is a member of the Research Group GNCS ruppo Nazionale per il Calcolo Scientificoof INdAM stituto Nazionale di Alta Matematica."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6423-6897","authenticated-orcid":true,"given":"Nicolas","family":"Gillis","sequence":"additional","affiliation":[{"name":"University of Mons, Mons, Belgium.\u00a0GB is a member of the Research Group GNCS ruppo Nazionale per il Calcolo Scientificoof INdAM stituto Nazionale di Alta Matematica."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,12,10]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1354982"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7439(01)00119-8"},{"key":"ref3","unstructured":"S. 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Fu, Detecting overlapping and correlated communities without pure nodes: Identifiability and algorithm, in Proceedings of the International Conference on Machine Learning, 2019, pp. 2859\u20132868."},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2013.2285514"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1038\/44565"},{"key":"ref24","doi-asserted-by":"crossref","unstructured":"V. Leplat, A. M. Ang, and N. 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