{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T16:02:48Z","timestamp":1784390568193,"version":"3.55.0"},"reference-count":56,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["101085607"],"award-info":[{"award-number":["101085607"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning.\u00a0A key property of many tensor decompositions, such as the canonical polyadic decomposition, is identifiability:\u00a0the factors are unique, up to trivial scaling and permutation ambiguities. This allows one to recover the groundtruth sources that generated the data.\u00a0The Tucker decomposition (TD) is a central and widely used tensor decomposition model.\u00a0However, it is in general not identifiable.\u00a0In this paper, we study the identifiability of the nonnegative TD (nTD). By adapting and extending identifiability results of nonnegative matrix factorization, we provide uniqueness results for nTD. Our results require the nonnegative matrix factors to have some degree of sparsity (namely, satisfy the separability condition, or the sufficiently scattered condition), while the core tensor only needs to have some slices (or linear combinations of them) or unfoldings with full column rank (but does not need to be nonnegative). Under such conditions, we derive several procedures, using either unfoldings or slices of the input tensor, to obtain identifiable nTDs by minimizing the volume of unfoldings or slices of the core tensor.<\/jats:p>","DOI":"10.1137\/25m1761914","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T07:01:26Z","timestamp":1783926086000},"page":"1210-1252","source":"Crossref","is-referenced-by-count":1,"title":["Identifiability of Nonnegative Tucker Decompositions\u2014Part I: Theory"],"prefix":"10.1137","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8233-8440","authenticated-orcid":true,"given":"Subhayan","family":"Saha","sequence":"first","affiliation":[{"name":"Department of Mathematics and Operational Research, University of Mons, Rue de Houdain 9, 7000 Mons, Belgium."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0504-7361","authenticated-orcid":true,"given":"Giovanni","family":"Barbarino","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Integradas, Facultad de Ciencias Experimentales, Universidad de Huelva, campus El Carmen, Huelva 21007, Spain. GB is member of the Research Group GNCS (Gruppo Nazionale per il Calcolo Scientifico) of INdAM (Istituto 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":"Department of Mathematics and Operational Research, University of Mons, Rue de Houdain 9, 7000 Mons, Belgium."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1354982"},{"key":"ref2","first-page":"1","volume":"120","author":"Agterberg J.","year":"2024","journal-title":"J. Amer. Statist. Assoc."},{"key":"ref3","first-page":"1981","volume-title":"J. Mach. Learn. Res.","volume":"9","author":"Airoldi E. 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