{"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/tensor-networks-for-dimensionality-reduction","title":"Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives","arxiv_id":"1708.09165","date":"2017-08-30","proceeding":null,"authors":["A. Cichocki","A-H. Phan","Q. Zhao","N. Lee","I. V. Oseledets","M. Sugiyama","D. Mandic"],"abstract":"Part 2 of this monograph builds on the introduction to tensor networks and\ntheir operations presented in Part 1. It focuses on tensor network models for\nsuper-compressed higher-order representation of data/parameters and related\ncost functions, while providing an outline of their applications in machine\nlearning and data analytics. A particular emphasis is on the tensor train (TT)\nand Hierarchical Tucker (HT) decompositions, and their physically meaningful\ninterpretations which reflect the scalability of the tensor network approach.\nThrough a graphical approach, we also elucidate how, by virtue of the\nunderlying low-rank tensor approximations and sophisticated contractions of\ncore tensors, tensor networks have the ability to perform distributed\ncomputations on otherwise prohibitively large volumes of data/parameters,\nthereby alleviating or even eliminating the curse of dimensionality. The\nusefulness of this concept is illustrated over a number of applied areas,\nincluding generalized regression and classification (support tensor machines,\ncanonical correlation analysis, higher order partial least squares),\ngeneralized eigenvalue decomposition, Riemannian optimization, and in the\noptimization of deep neural networks. Part 1 and Part 2 of this work can be\nused either as stand-alone separate texts, or indeed as a conjoint\ncomprehensive review of the exciting field of low-rank tensor networks and\ntensor decompositions.","url_abs":"http://arxiv.org/abs/1708.09165v1","url_pdf":"http://arxiv.org/pdf/1708.09165v1.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":"tensor-networks-for-dimensionality-reduction","repo_url":"https://github.com/rballester/ttrecipes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"riemannian-optimization","task_name":"Riemannian optimization"},{"task_slug":"tensor-networks","task_name":"Tensor Networks"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1708.09165","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}