{"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/provable-tensor-factorization-with-missing","title":"Provable Tensor Factorization with Missing Data","arxiv_id":"1406.2784","date":"2014-06-11","proceeding":"NeurIPS 2014 12","authors":["Prateek Jain","Sewoong Oh"],"abstract":"We study the problem of low-rank tensor factorization in the presence of\nmissing data. We ask the following question: how many sampled entries do we\nneed, to efficiently and exactly reconstruct a tensor with a low-rank\northogonal decomposition? We propose a novel alternating minimization based\nmethod which iteratively refines estimates of the singular vectors. We show\nthat under certain standard assumptions, our method can recover a three-mode\n$n\\times n\\times n$ dimensional rank-$r$ tensor exactly from $O(n^{3/2} r^5\n\\log^4 n)$ randomly sampled entries. In the process of proving this result, we\nsolve two challenging sub-problems for tensors with missing data. First, in the\nprocess of analyzing the initialization step, we prove a generalization of a\ncelebrated result by Szemer\\'edie et al. on the spectrum of random graphs.\nNext, we prove global convergence of alternating minimization with a good\ninitialization. Simulations suggest that the dependence of the sample size on\ndimensionality $n$ is indeed tight.","url_abs":"http://arxiv.org/abs/1406.2784v1","url_pdf":"http://arxiv.org/pdf/1406.2784v1.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":"provable-tensor-factorization-with-missing","repo_url":"https://github.com/RuiLin0212/MiSC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1406.2784","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}