{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-exact-solution-to-rank-1-l1-norm-tucker2","title":"The Exact Solution to Rank-1 L1-norm TUCKER2 Decomposition","arxiv_id":"1710.11306","date":"2017-10-31","proceeding":null,"authors":["Panos P. Markopoulos","Dimitris G. Chachlakis","Evangelos E. Papalexakis"],"abstract":"We study rank-1 {L1-norm-based TUCKER2} (L1-TUCKER2) decomposition of 3-way\ntensors, treated as a collection of $N$ $D \\times M$ matrices that are to be\njointly decomposed. Our contributions are as follows. i) We prove that the\nproblem is equivalent to combinatorial optimization over $N$ antipodal-binary\nvariables. ii) We derive the first two algorithms in the literature for its\nexact solution. The first algorithm has cost exponential in $N$; the second one\nhas cost polynomial in $N$ (under a mild assumption). Our algorithms are\naccompanied by formal complexity analysis. iii) We conduct numerical studies to\ncompare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD,\nHOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. Our studies show that L1-TUCKER2\noutperforms (in tensor approximation) all the above counterparts when the\nprocessed data are outlier corrupted.","url_abs":"http://arxiv.org/abs/1710.11306v1","url_pdf":"http://arxiv.org/pdf/1710.11306v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-exact-solution-to-rank-1-l1-norm-tucker2","repo_url":"https://github.com/dgchachlakis/The-exact-solution-to-rank-1-L1-norm-Tucker2-decomposition","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}