{"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/tucker-operatorname-l-2e-robust-low-rank","title":"Robust Low-rank Tensor Decomposition with the $\\operatorname{L_2}$ Criterion","arxiv_id":"2208.11806","date":"2022-08-25","proceeding":null,"authors":["Qiang Heng","Eric C. Chi","Yufeng Liu"],"abstract":"The growing prevalence of tensor data, or multiway arrays, in science and engineering applications motivates the need for tensor decompositions that are robust against outliers. In this paper, we present a robust Tucker decomposition estimator based on the $\\operatorname{L_2}$ criterion, called the Tucker-$\\operatorname{L_2E}$. Our numerical experiments demonstrate that Tucker-$\\operatorname{L_2E}$ has empirically stronger recovery performance in more challenging high-rank scenarios compared with existing alternatives. The appropriate Tucker-rank can be selected in a data-driven manner with cross-validation or hold-out validation. The practical effectiveness of Tucker-$\\operatorname{L_2E}$ is validated on real data applications in fMRI tensor denoising, PARAFAC analysis of fluorescence data, and feature extraction for classification of corrupted images.","url_abs":"https://arxiv.org/abs/2208.11806v3","url_pdf":"https://arxiv.org/pdf/2208.11806v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"tucker-operatorname-l-2e-robust-low-rank","repo_url":"https://github.com/qhengncsu/tuckerl2e","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}