{"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/euler-characteristic-tools-for-topological","title":"Euler Characteristic Tools For Topological Data Analysis","arxiv_id":"2303.14040","date":"2023-03-24","proceeding":null,"authors":["Olympio Hacquard","Vadim Lebovici"],"abstract":"In this article, we study Euler characteristic techniques in topological data analysis. Pointwise computing the Euler characteristic of a family of simplicial complexes built from data gives rise to the so-called Euler characteristic profile. We show that this simple descriptor achieve state-of-the-art performance in supervised tasks at a very low computational cost. Inspired by signal analysis, we compute hybrid transforms of Euler characteristic profiles. These integral transforms mix Euler characteristic techniques with Lebesgue integration to provide highly efficient compressors of topological signals. As a consequence, they show remarkable performances in unsupervised settings. On the qualitative side, we provide numerous heuristics on the topological and geometric information captured by Euler profiles and their hybrid transforms. Finally, we prove stability results for these descriptors as well as asymptotic guarantees in random settings.","url_abs":"https://arxiv.org/abs/2303.14040v3","url_pdf":"https://arxiv.org/pdf/2303.14040v3.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":"euler-characteristic-tools-for-topological","repo_url":"https://github.com/vadimlebovici/eulearning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2303.14040","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2303.14040"}},"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/vadimlebovici/eulearning","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":8},"by_repo_kind":{"official":{"samples":8,"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":"13940860202e00b0","entry":"codensity","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/utils.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/utils.py","link_basis":"harvester_set","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":"13940860202e00b0"}},{"code_sha256_prefix":"1fc16af3efec29b3","entry":"compute_euler_curve","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/descriptors.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/descriptors.py","link_basis":"harvester_set","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":"1fc16af3efec29b3"}},{"code_sha256_prefix":"0ea7eff27e5ea9b1","entry":"compute_euler_profile","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/descriptors.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/descriptors.py","link_basis":"harvester_set","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":"0ea7eff27e5ea9b1"}},{"code_sha256_prefix":"fe67db6839de3703","entry":"compute_hybrid_transform","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/descriptors.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/descriptors.py","link_basis":"harvester_set","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":"fe67db6839de3703"}},{"code_sha256_prefix":"61ccf4504905ed52","entry":"compute_vertvals_from_edgevals","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/utils.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/utils.py","link_basis":"harvester_set","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":"61ccf4504905ed52"}},{"code_sha256_prefix":"c9c089959a711070","entry":"gen_dense_lines_with_noise","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/datasets.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/datasets.py","link_basis":"harvester_set","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":"c9c089959a711070"}},{"code_sha256_prefix":"c6d396f3340e280c","entry":"gen_torus_non_unif","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/datasets.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/datasets.py","link_basis":"harvester_set","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":"c6d396f3340e280c"}},{"code_sha256_prefix":"788b96d5035ec760","entry":"gen_torus_unif","repo":"vadimlebovici/eulearning","repo_kind":"official","path":"eulearning/datasets.py","file_url":"https://github.com/vadimlebovici/eulearning/blob/HEAD/eulearning/datasets.py","link_basis":"harvester_set","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":"788b96d5035ec760"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}