{"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/a-distributed-frank-wolfe-framework-for","title":"A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm","arxiv_id":"1712.07495","date":"2017-12-20","proceeding":null,"authors":["Wenjie Zheng","Aurélien Bellet","Patrick Gallinari"],"abstract":"We consider the problem of learning a high-dimensional but low-rank matrix\nfrom a large-scale dataset distributed over several machines, where\nlow-rankness is enforced by a convex trace norm constraint. We propose\nDFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank\nstructure of its updates to achieve efficiency in time, memory and\ncommunication usage. The step at the heart of DFW-Trace is solved approximately\nusing a distributed version of the power method. We provide a theoretical\nanalysis of the convergence of DFW-Trace, showing that we can ensure sublinear\nconvergence in expectation to an optimal solution with few power iterations per\nepoch. We implement DFW-Trace in the Apache Spark distributed programming\nframework and validate the usefulness of our approach on synthetic and real\ndata, including the ImageNet dataset with high-dimensional features extracted\nfrom a deep neural network.","url_abs":"http://arxiv.org/abs/1712.07495v2","url_pdf":"http://arxiv.org/pdf/1712.07495v2.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":"a-distributed-frank-wolfe-framework-for","repo_url":"https://github.com/WenjieZ/distributed-frank-wolfe","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1712.07495","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}