{"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/kernel-method-for-persistence-diagrams-via","title":"Kernel method for persistence diagrams via kernel embedding and weight factor","arxiv_id":"1706.03472","date":"2017-06-12","proceeding":null,"authors":["Genki Kusano","Kenji Fukumizu","Yasuaki Hiraoka"],"abstract":"Topological data analysis is an emerging mathematical concept for\ncharacterizing shapes in multi-scale data. In this field, persistence diagrams\nare widely used as a descriptor of the input data, and can distinguish robust\nand noisy topological properties. Nowadays, it is highly desired to develop a\nstatistical framework on persistence diagrams to deal with practical data. This\npaper proposes a kernel method on persistence diagrams. A theoretical\ncontribution of our method is that the proposed kernel allows one to control\nthe effect of persistence, and, if necessary, noisy topological properties can\nbe discounted in data analysis. Furthermore, the method provides a fast\napproximation technique. The method is applied into several problems including\npractical data in physics, and the results show the advantage compared to the\nexisting kernel method on persistence diagrams.","url_abs":"http://arxiv.org/abs/1706.03472v1","url_pdf":"http://arxiv.org/pdf/1706.03472v1.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":"kernel-method-for-persistence-diagrams-via","repo_url":"https://github.com/genki-kusano/python-pwgk","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"graph-classification","task_name":"Graph Classification"},{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-classification-on-neuron-average","task":"Graph Classification","dataset":"NEURON-Average","model":"PWGK","rank_in_archive_order":5,"of":5,"metrics":{"Accuracy":"62.80"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-neuron-binary","task":"Graph Classification","dataset":"NEURON-BINARY","model":"PWGK","rank_in_archive_order":5,"of":5,"metrics":{"Accuracy":"80.1"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-neuron-multi","task":"Graph Classification","dataset":"NEURON-MULTI","model":"PWGK","rank_in_archive_order":4,"of":5,"metrics":{"Accuracy":"45.5"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.03472","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}