{"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/knot-invariants-and-their-relations-a","title":"Mapper-type algorithms for complex data and relations","arxiv_id":"2109.00831","date":"2021-09-02","proceeding":null,"authors":["Paweł Dłotko","Davide Gurnari","Radmila Sazdanovic"],"abstract":"Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to Ball Mapper that enable encoding of the structure, internal relations and symmetries of the point cloud. Moreover, the strengths of Mapper and Ball Mapper constructions are combined to create a tool for comparing high dimensional data descriptors of a single dataset. This new hybrid algorithm, Mapper on Ball Mapper, is applicable to high dimensional lens functions. As a proof of concept we include applications to knot and game theory, as well as material science and cancer research.","url_abs":"https://arxiv.org/abs/2109.00831v2","url_pdf":"https://arxiv.org/pdf/2109.00831v2.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":"knot-invariants-and-their-relations-a","repo_url":"https://github.com/dgurnari/knotsbm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"},{"task_slug":"type","task_name":"Vocal Bursts Type Prediction"}],"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}