{"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/introduction-to-tensor-decompositions-and","title":"Introduction to Tensor Decompositions and their Applications in Machine Learning","arxiv_id":"1711.10781","date":"2017-11-29","proceeding":null,"authors":["Stephan Rabanser","Oleksandr Shchur","Stephan Günnemann"],"abstract":"Tensors are multidimensional arrays of numerical values and therefore\ngeneralize matrices to multiple dimensions. While tensors first emerged in the\npsychometrics community in the $20^{\\text{th}}$ century, they have since then\nspread to numerous other disciplines, including machine learning. Tensors and\ntheir decompositions are especially beneficial in unsupervised learning\nsettings, but are gaining popularity in other sub-disciplines like temporal and\nmulti-relational data analysis, too.\n  The scope of this paper is to give a broad overview of tensors, their\ndecompositions, and how they are used in machine learning. As part of this, we\nare going to introduce basic tensor concepts, discuss why tensors can be\nconsidered more rigid than matrices with respect to the uniqueness of their\ndecomposition, explain the most important factorization algorithms and their\nproperties, provide concrete examples of tensor decomposition applications in\nmachine learning, conduct a case study on tensor-based estimation of mixture\nmodels, talk about the current state of research, and provide references to\navailable software libraries.","url_abs":"http://arxiv.org/abs/1711.10781v1","url_pdf":"http://arxiv.org/pdf/1711.10781v1.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":"introduction-to-tensor-decompositions-and","repo_url":"https://github.com/yidilozdemir/fmriBridge","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.10781","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}