{"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/riemannian-preconditioned-coordinate-descent","title":"Riemannian preconditioned coordinate descent for low multi-linear rank approximation","arxiv_id":"2109.01632","date":"2021-09-03","proceeding":null,"authors":["Mohammad Hamed","Reshad Hosseini"],"abstract":"This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold. We use a Riemmanian coordinate descent method for solving the problem, and also provide a global convergence analysis matching that of the coordinate descent method in the Euclidean setting. We also show that each step of our method with the unit step-size is actually a step of the orthogonal iteration algorithm. Experimental results show the computational advantage of our method for high-dimensional tensors.","url_abs":"https://arxiv.org/abs/2109.01632v2","url_pdf":"https://arxiv.org/pdf/2109.01632v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"riemannian-preconditioned-coordinate-descent","repo_url":"https://github.com/utvisionlab/rpcd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}