{"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/optimization-of-inter-group-criteria-for-1","title":"Optimization of Inter-group Criteria for Clustering with Minimum Size Constraints","arxiv_id":"2401.07091","date":"2024-01-13","proceeding":"NeurIPS 2023 11","authors":["Eduardo S. Laber","Lucas Murtinho"],"abstract":"Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees for optimizing the former. However, the optimization of inter-group criteria is much less understood. Here, we contribute to the state-of-the-art of this literature by devising algorithms with provable guarantees for the maximization of two natural inter-group criteria, namely the minimum spacing and the minimum spanning tree spacing. The former is the minimum distance between points in different groups while the latter captures separability through the cost of the minimum spanning tree that connects all groups. We obtain results for both the unrestricted case, in which no constraint on the clusters is imposed, and for the constrained case where each group is required to have a minimum number of points. Our constraint is motivated by the fact that the popular Single Linkage, which optimizes both criteria in the unrestricted case, produces clusterings with many tiny groups. To complement our work, we present an empirical study with 10 real datasets, providing evidence that our methods work very well in practical settings.","url_abs":"https://arxiv.org/abs/2401.07091v1","url_pdf":"https://arxiv.org/pdf/2401.07091v1.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":"optimization-of-inter-group-criteria-for-1","repo_url":"https://github.com/lmurtinho/sizeconstrainedspacing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2401.07091","atlas_url":"https://app.syntology.ai/?focus=2401.07091","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2401.07091"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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":"deterministic:regex_extraction","url":"https://github.com/lmurtinho/SizeConstrainedSpacing","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lmurtinho/sizeconstrainedspacing","reach":{"status":"ok"}}],"summary":{"ran":4,"ran_draft_wrong":1,"ran_fixture":1,"unverified":1},"by_repo_kind":{"official":{"samples":7,"ran":6,"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":7,"samples":[{"code_sha256_prefix":"da2c15d4022aa83c","entry":"get_all_dists","repo":"lmurtinho/sizeconstrainedspacing","repo_kind":"official","path":"get_scores.py","file_url":"https://github.com/lmurtinho/sizeconstrainedspacing/blob/HEAD/get_scores.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"da2c15d4022aa83c"}},{"code_sha256_prefix":"f9c31c690e8a7f31","entry":"get_data","repo":"lmurtinho/sizeconstrainedspacing","repo_kind":"official","path":"get_scores.py","file_url":"https://github.com/lmurtinho/sizeconstrainedspacing/blob/HEAD/get_scores.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f9c31c690e8a7f31"}},{"code_sha256_prefix":"c62a4f3fa4a95892","entry":"get_dataset","repo":"lmurtinho/sizeconstrainedspacing","repo_kind":"official","path":"get_datasets.py","file_url":"https://github.com/lmurtinho/sizeconstrainedspacing/blob/HEAD/get_datasets.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c62a4f3fa4a95892"}},{"code_sha256_prefix":"a88f3808a3436a2e","entry":"get_model","repo":"lmurtinho/SizeConstrainedSpacing","repo_kind":"official","path":"generate_models.py","file_url":"https://github.com/lmurtinho/SizeConstrainedSpacing/blob/HEAD/generate_models.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a88f3808a3436a2e"}},{"code_sha256_prefix":"604b6c71e4a920ac","entry":"get_mst_edges","repo":"lmurtinho/sizeconstrainedspacing","repo_kind":"official","path":"get_scores.py","file_url":"https://github.com/lmurtinho/sizeconstrainedspacing/blob/HEAD/get_scores.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"604b6c71e4a920ac"}},{"code_sha256_prefix":"22ca376c9e21f3ed","entry":"single_model_result","repo":"lmurtinho/SizeConstrainedSpacing","repo_kind":"official","path":"generate_models.py","file_url":"https://github.com/lmurtinho/SizeConstrainedSpacing/blob/HEAD/generate_models.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"22ca376c9e21f3ed"}},{"code_sha256_prefix":"257694a3959e5b38","entry":"get_bz","repo":"lmurtinho/sizeconstrainedspacing","repo_kind":"official","path":"get_datasets.py","file_url":"https://github.com/lmurtinho/sizeconstrainedspacing/blob/HEAD/get_datasets.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"257694a3959e5b38"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}