{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:E2CDZ5VUBDAZNVP3R3CXXTCDP4","short_pith_number":"pith:E2CDZ5VU","schema_version":"1.0","canonical_sha256":"26843cf6b408c196d5fb8ec57bcc437f393d696bffa3fc8b0aebf3b93b1df714","source":{"kind":"arxiv","id":"1901.02393","version":2},"attestation_state":"computed","paper":{"title":"Fair Algorithms for Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Deeparnab Chakrabarty, Maryam Negahbani, Nicolas J. Flores, Suman K. Bera","submitted_at":"2019-01-08T16:39:16Z","abstract_excerpt":"We study the problem of finding low-cost Fair Clusterings in data where each data point may belong to many protected groups. Our work significantly generalizes the seminal work of Chierichetti et.al. (NIPS 2017) as follows.\n  - We allow the user to specify the parameters that define fair representation. More precisely, these parameters define the maximum over- and minimum under-representation of any group in any cluster.\n  - Our clustering algorithm works on any $\\ell_p$-norm objective (e.g. $k$-means, $k$-median, and $k$-center). Indeed, our algorithm transforms any vanilla clustering solutio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.02393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-01-08T16:39:16Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f0ef37509cf7d243e3a4f3a6ea5a37119ef9c4c6980ca58b92d38bac489c0db9","abstract_canon_sha256":"5f985928a8c6307def1b2cb9de66b35056853215be9ca1eff3add1836c1f9f5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:16.971009Z","signature_b64":"zFnLqh4i0cSZlpZ11Ypear6vZwvu0ZUNRpgNxqzfz3jWmmXD9uhZI8GEApzGZeRv9nSK2Y6GVtM/JzOWR8ygAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26843cf6b408c196d5fb8ec57bcc437f393d696bffa3fc8b0aebf3b93b1df714","last_reissued_at":"2026-05-17T23:43:16.970535Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:16.970535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fair Algorithms for Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Deeparnab Chakrabarty, Maryam Negahbani, Nicolas J. Flores, Suman K. Bera","submitted_at":"2019-01-08T16:39:16Z","abstract_excerpt":"We study the problem of finding low-cost Fair Clusterings in data where each data point may belong to many protected groups. Our work significantly generalizes the seminal work of Chierichetti et.al. (NIPS 2017) as follows.\n  - We allow the user to specify the parameters that define fair representation. More precisely, these parameters define the maximum over- and minimum under-representation of any group in any cluster.\n  - Our clustering algorithm works on any $\\ell_p$-norm objective (e.g. $k$-means, $k$-median, and $k$-center). Indeed, our algorithm transforms any vanilla clustering solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02393","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.02393","created_at":"2026-05-17T23:43:16.970604+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02393v2","created_at":"2026-05-17T23:43:16.970604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02393","created_at":"2026-05-17T23:43:16.970604+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2CDZ5VUBDAZ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2CDZ5VUBDAZNVP3","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2CDZ5VU","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4","json":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4.json","graph_json":"https://pith.science/api/pith-number/E2CDZ5VUBDAZNVP3R3CXXTCDP4/graph.json","events_json":"https://pith.science/api/pith-number/E2CDZ5VUBDAZNVP3R3CXXTCDP4/events.json","paper":"https://pith.science/paper/E2CDZ5VU"},"agent_actions":{"view_html":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4","download_json":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4.json","view_paper":"https://pith.science/paper/E2CDZ5VU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02393&json=true","fetch_graph":"https://pith.science/api/pith-number/E2CDZ5VUBDAZNVP3R3CXXTCDP4/graph.json","fetch_events":"https://pith.science/api/pith-number/E2CDZ5VUBDAZNVP3R3CXXTCDP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4/action/storage_attestation","attest_author":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4/action/author_attestation","sign_citation":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4/action/citation_signature","submit_replication":"https://pith.science/pith/E2CDZ5VUBDAZNVP3R3CXXTCDP4/action/replication_record"}},"created_at":"2026-05-17T23:43:16.970604+00:00","updated_at":"2026-05-17T23:43:16.970604+00:00"}