{"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-factorization-via-matrix-factorization","title":"Tensor Factorization via Matrix Factorization","arxiv_id":"1501.07320","date":"2015-01-29","proceeding":null,"authors":["Volodymyr Kuleshov","Arun Tejasvi Chaganty","Percy Liang"],"abstract":"Tensor factorization arises in many machine learning applications, such\nknowledge base modeling and parameter estimation in latent variable models.\nHowever, numerical methods for tensor factorization have not reached the level\nof maturity of matrix factorization methods. In this paper, we propose a new\nmethod for CP tensor factorization that uses random projections to reduce the\nproblem to simultaneous matrix diagonalization. Our method is conceptually\nsimple and also applies to non-orthogonal and asymmetric tensors of arbitrary\norder. We prove that a small number random projections essentially preserves\nthe spectral information in the tensor, allowing us to remove the dependence on\nthe eigengap that plagued earlier tensor-to-matrix reductions. Experimentally,\nour method outperforms existing tensor factorization methods on both simulated\ndata and two real datasets.","url_abs":"http://arxiv.org/abs/1501.07320v2","url_pdf":"http://arxiv.org/pdf/1501.07320v2.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-factorization-via-matrix-factorization","repo_url":"https://worksheets.codalab.org/worksheets/0x56dc93bcd3a647b197ad6e4b9d56f336","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1501.07320","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}