{"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/a-closed-form-solution-to-best-rank-1-tensor","title":"Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation","arxiv_id":"2103.02898","date":"2021-03-04","proceeding":"NeurIPS 2021 12","authors":["Kazu Ghalamkari","Mahito Sugiyama"],"abstract":"We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First, we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating each tensor as a probability distribution. Second, we theoretically provide a sufficient condition for distribution parameters to reduce Tucker ranks of tensors; interestingly, this sufficient condition can be achieved by iterative application of the mean-field approximation. Since the mean-field approximation is always given as a closed formula, our findings lead to a fast low-rank approximation algorithm without using a gradient method. We empirically demonstrate that our algorithm is faster than the existing non-negative Tucker rank reduction methods and achieves competitive or better approximation of given tensors.","url_abs":"https://arxiv.org/abs/2103.02898v3","url_pdf":"https://arxiv.org/pdf/2103.02898v3.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":"a-closed-form-solution-to-best-rank-1-tensor","repo_url":"https://github.com/gkazunii/Legendre-tucker-rank-reduction","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[{"method_slug":"tucker","method_name":"TuckER"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2103.02898","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}