{"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/principal-manifolds-and-graphs-in-practice","title":"Principal manifolds and graphs in practice: from molecular biology to dynamical systems","arxiv_id":"1001.1122","date":"2010-01-07","proceeding":null,"authors":["A. N. Gorban","A. Zinovyev"],"abstract":"We present several applications of non-linear data modeling, using principal\nmanifolds and principal graphs constructed using the metaphor of elasticity\n(elastic principal graph approach). These approaches are generalizations of the\nKohonen's self-organizing maps, a class of artificial neural networks. On\nseveral examples we show advantages of using non-linear objects for data\napproximation in comparison to the linear ones. We propose four numerical\ncriteria for comparing linear and non-linear mappings of datasets into the\nspaces of lower dimension. The examples are taken from comparative political\nscience, from analysis of high-throughput data in molecular biology, from\nanalysis of dynamical systems.","url_abs":"http://arxiv.org/abs/1001.1122v2","url_pdf":"http://arxiv.org/pdf/1001.1122v2.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":"principal-manifolds-and-graphs-in-practice","repo_url":"https://github.com/auranic/Elastic-principal-graphs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"principal-manifolds-and-graphs-in-practice","repo_url":"https://github.com/sysbio-curie/ElPiGraph.M","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}