{"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/dtm-based-filtrations","title":"DTM-based Filtrations","arxiv_id":"1811.04757","date":"2018-11-12","proceeding":null,"authors":["Hirokazu Anai","Frédéric Chazal","Marc Glisse","Yuichi Ike","Hiroya Inakoshi","Raphaël Tinarrage","Yuhei Umeda"],"abstract":"Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Cech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.","url_abs":"https://arxiv.org/abs/1811.04757v3","url_pdf":"https://arxiv.org/pdf/1811.04757v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"dtm-based-filtrations","repo_url":"https://github.com/GUDHI/TDA-tutorial","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"dtm-based-filtrations","repo_url":"https://github.com/raphaeltinarrage/DTM-Filtrations","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.04757","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1811.04757"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/GUDHI/TDA-tutorial","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/raphaeltinarrage/DTM-Filtrations","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":9},"by_repo_kind":{"official":{"samples":9,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"f4c6f3ffef3ea12f","entry":"DTM","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_dtm.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_dtm.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f4c6f3ffef3ea12f"}},{"code_sha256_prefix":"a07a2a32db9621b7","entry":"WeightedRipsFiltrationValue","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_dtm.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_dtm.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a07a2a32db9621b7"}},{"code_sha256_prefix":"5f5be53c7ac9dfa8","entry":"hausd_interval","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/persistence_statistics.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/persistence_statistics.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5f5be53c7ac9dfa8"}},{"code_sha256_prefix":"8b8d3ffe92babb3a","entry":"init_c","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_quantization.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_quantization.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8b8d3ffe92babb3a"}},{"code_sha256_prefix":"4225d2c56e9f4789","entry":"quantization","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_quantization.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_quantization.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"4225d2c56e9f4789"}},{"code_sha256_prefix":"7be86e43fe3c94e0","entry":"sample_circle","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_epd.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_epd.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7be86e43fe3c94e0"}},{"code_sha256_prefix":"a8315cc4eabef8cd","entry":"sample_noise","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_epd.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_epd.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a8315cc4eabef8cd"}},{"code_sha256_prefix":"2c1d685ea7e6e97c","entry":"sample_torus","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/utils_epd.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/utils_epd.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2c1d685ea7e6e97c"}},{"code_sha256_prefix":"17ff6d0ee90090ae","entry":"truncated_simplex_tree","repo":"GUDHI/TDA-tutorial","repo_kind":"official","path":"tutorials/utils/persistence_statistics.py","file_url":"https://github.com/GUDHI/TDA-tutorial/blob/HEAD/tutorials/utils/persistence_statistics.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"17ff6d0ee90090ae"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}