{"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/persistence-diagrams-with-linear-machine","title":"Persistence Diagrams with Linear Machine Learning Models","arxiv_id":"1706.10082","date":"2017-06-30","proceeding":null,"authors":["Ippei Obayashi","Yasuaki Hiraoka"],"abstract":"Persistence diagrams have been widely recognized as a compact descriptor for\ncharacterizing multiscale topological features in data. When many datasets are\navailable, statistical features embedded in those persistence diagrams can be\nextracted by applying machine learnings. In particular, the ability for\nexplicitly analyzing the inverse in the original data space from those\nstatistical features of persistence diagrams is significantly important for\npractical applications. In this paper, we propose a unified method for the\ninverse analysis by combining linear machine learning models with persistence\nimages. The method is applied to point clouds and cubical sets, showing the\nability of the statistical inverse analysis and its advantages.","url_abs":"http://arxiv.org/abs/1706.10082v2","url_pdf":"http://arxiv.org/pdf/1706.10082v2.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":"persistence-diagrams-with-linear-machine","repo_url":"https://github.com/sauln/persim","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"persistence-diagrams-with-linear-machine","repo_url":"https://github.com/scikit-tda/persim","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.10082","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}