{"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/fitting-low-rank-tensors-in-constant-time","title":"Fitting Low-Rank Tensors in Constant Time","arxiv_id":null,"date":"2017-12-01","proceeding":"NeurIPS 2017 12","authors":["Kohei Hayashi","Yuichi Yoshida"],"abstract":"In this paper, we develop an algorithm that approximates the residual error of Tucker decomposition, one of the most popular tensor decomposition methods, with a provable guarantee.  Given an order-$K$ tensor $X\\in\\mathbb{R}^{N_1\\times\\cdots\\times N_K}$, our algorithm randomly samples a constant number $s$ of indices for each mode and creates a ``mini'' tensor $\\tilde{X}\\in\\mathbb{R}^{s\\times\\cdots\\times s}$, whose elements are given by the intersection of the sampled indices on $X$.  Then, we show that the residual error of the Tucker decomposition of $\\tilde{X}$ is sufficiently close to that of $X$ with high probability.  This result implies that we can figure out how much we can fit a low-rank tensor to $X$ \\emph{in constant time}, regardless of the size of $X$. This is useful for guessing the favorable rank of Tucker decomposition.  Finally, we demonstrate how the sampling method works quickly and accurately using multiple real datasets.","url_abs":"http://papers.nips.cc/paper/6841-fitting-low-rank-tensors-in-constant-time","url_pdf":"http://papers.nips.cc/paper/6841-fitting-low-rank-tensors-in-constant-time.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":"fitting-low-rank-tensors-in-constant-time","repo_url":"https://github.com/hayasick/CTFT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"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}