{"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/deterministic-tensor-completion-with","title":"Deterministic tensor completion with hypergraph expanders","arxiv_id":"1910.10692","date":"2019-10-23","proceeding":null,"authors":["Kameron Decker Harris","Yizhe Zhu"],"abstract":"We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows that the number of samples required to approximately recover an order-$t$ tensor with at most $n$ entries per dimension is linear in $n$, under the assumption that the rank and order of the tensor are $O(1)$. As steps in our proof, we find a new expander mixing lemma for a $t$-partite, $t$-uniform regular hypergraph model, and prove several new properties about tensor max-quasinorm. To the best of our knowledge, this is the first deterministic analysis of tensor completion. We develop a practical algorithm that solves a relaxed version of the max-quasinorm minimization problem, and we demonstrate its efficacy with numerical experiments.","url_abs":"https://arxiv.org/abs/1910.10692v4","url_pdf":"https://arxiv.org/pdf/1910.10692v4.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":"deterministic-tensor-completion-with","repo_url":"https://github.com/kharris/max-qnorm-tensor-completion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"deterministic-tensor-completion-with","repo_url":"https://github.com/kamdh/max-qnorm-tensor-completion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"lemma","task_name":"LEMMA"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}