{"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/sliced-wasserstein-kernel-for-persistence","title":"Sliced Wasserstein Kernel for Persistence Diagrams","arxiv_id":"1706.03358","date":"2017-06-11","proceeding":"ICML 2017 8","authors":["Mathieu Carrière","Marco Cuturi","Steve Oudot"],"abstract":"Persistence diagrams (PDs) play a key role in topological data analysis\n(TDA), in which they are routinely used to describe topological properties of\ncomplicated shapes. PDs enjoy strong stability properties and have proven their\nutility in various learning contexts. They do not, however, live in a space\nnaturally endowed with a Hilbert structure and are usually compared with\nspecific distances, such as the bottleneck distance. To incorporate PDs in a\nlearning pipeline, several kernels have been proposed for PDs with a strong\nemphasis on the stability of the RKHS distance w.r.t. perturbations of the PDs.\nIn this article, we use the Sliced Wasserstein approximation SW of the\nWasserstein distance to define a new kernel for PDs, which is not only provably\nstable but also provably discriminative (depending on the number of points in\nthe PDs) w.r.t. the Wasserstein distance $d_1$ between PDs. We also demonstrate\nits practicality, by developing an approximation technique to reduce kernel\ncomputation time, and show that our proposal compares favorably to existing\nkernels for PDs on several benchmarks.","url_abs":"http://arxiv.org/abs/1706.03358v3","url_pdf":"http://arxiv.org/pdf/1706.03358v3.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":[],"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":"SW","rank_in_archive_order":3,"of":5,"metrics":{"Accuracy":"71.20"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-neuron-binary","task":"Graph Classification","dataset":"NEURON-BINARY","model":"SW","rank_in_archive_order":3,"of":5,"metrics":{"Accuracy":"85.1"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-neuron-multi","task":"Graph Classification","dataset":"NEURON-MULTI","model":"SW","rank_in_archive_order":2,"of":5,"metrics":{"Accuracy":"57.3"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.03358","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}