{"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/efficient-sparse-representation-of-manifold","title":"Efficient, sparse representation of manifold distance matrices for classical scaling","arxiv_id":"1705.10887","date":"2017-05-30","proceeding":"CVPR 2018 6","authors":["Javier S. Turek","Alexander Huth"],"abstract":"Geodesic distance matrices can reveal shape properties that are largely\ninvariant to non-rigid deformations, and thus are often used to analyze and\nrepresent 3-D shapes. However, these matrices grow quadratically with the\nnumber of points. Thus for large point sets it is common to use a low-rank\napproximation to the distance matrix, which fits in memory and can be\nefficiently analyzed using methods such as multidimensional scaling (MDS). In\nthis paper we present a novel sparse method for efficiently representing\ngeodesic distance matrices using biharmonic interpolation. This method exploits\nknowledge of the data manifold to learn a sparse interpolation operator that\napproximates distances using a subset of points. We show that our method is 2x\nfaster and uses 20x less memory than current leading methods for solving MDS on\nlarge point sets, with similar quality. This enables analyses of large point\nsets that were previously infeasible.","url_abs":"http://arxiv.org/abs/1705.10887v2","url_pdf":"http://arxiv.org/pdf/1705.10887v2.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":"efficient-sparse-representation-of-manifold","repo_url":"https://github.com/alexhuth/BHA","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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}