{"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/high-dimension-tensor-completion-via-gradient","title":"High-dimension Tensor Completion via Gradient-based Optimization Under Tensor-train Format","arxiv_id":"1804.01983","date":"2018-04-05","proceeding":null,"authors":["Longhao Yuan","Qibin Zhao","Lihua Gui","Jianting Cao"],"abstract":"Tensor train (TT) decomposition has drawn people's attention due to its\npowerful representation ability and performance stability in high-order\ntensors. In this paper, we propose a novel approach to recover the missing\nentries of incomplete data represented by higher-order tensors. We attempt to\nfind the low-rank TT decomposition of the incomplete data which captures the\nlatent features of the whole data and then reconstruct the missing entries. By\napplying gradient descent algorithms, tensor completion problem is efficiently\nsolved by optimization models. We propose two TT-based algorithms: Tensor Train\nWeighted Optimization (TT-WOPT) and Tensor Train Stochastic Gradient Descent\n(TT-SGD) to optimize TT decomposition factors. In addition, a method named\nVisual Data Tensorization (VDT) is proposed to transform visual data into\nhigher-order tensors, resulting in the performance improvement of our\nalgorithms. The experiments in synthetic data and visual data show high\nefficiency and performance of our algorithms compared to the state-of-the-art\ncompletion algorithms, especially in high-order, high missing rate, and\nlarge-scale tensor completion situations.","url_abs":"http://arxiv.org/abs/1804.01983v3","url_pdf":"http://arxiv.org/pdf/1804.01983v3.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":"high-dimension-tensor-completion-via-gradient","repo_url":"https://github.com/yuanlonghao/T3C_tensor_completion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.01983","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}