{"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/legendre-decomposition-for-tensors","title":"Legendre Decomposition for Tensors","arxiv_id":"1802.04502","date":"2018-02-13","proceeding":"NeurIPS 2018 12","authors":["Mahito Sugiyama","Hiroyuki Nakahara","Koji Tsuda"],"abstract":"We present a novel nonnegative tensor decomposition method, called Legendre\ndecomposition, which factorizes an input tensor into a multiplicative\ncombination of parameters. Thanks to the well-developed theory of information\ngeometry, the reconstructed tensor is unique and always minimizes the KL\ndivergence from an input tensor. We empirically show that Legendre\ndecomposition can more accurately reconstruct tensors than other nonnegative\ntensor decomposition methods.","url_abs":"http://arxiv.org/abs/1802.04502v2","url_pdf":"http://arxiv.org/pdf/1802.04502v2.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":"legendre-decomposition-for-tensors","repo_url":"https://github.com/mahito-sugiyama/Legendre-decomposition","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1802.04502","atlas_url":"https://app.syntology.ai/?focus=1802.04502","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}