{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:267QVADYW4RD4BM7QAID7PVAKJ","short_pith_number":"pith:267QVADY","schema_version":"1.0","canonical_sha256":"d7bf0a8078b7223e059f80103fbea0525340d59ebb3cafc7dd855a5bb5a77fd0","source":{"kind":"arxiv","id":"1810.10134","version":2},"attestation_state":"computed","paper":{"title":"A Binary Optimization Approach for Constrained K-Means Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Anders Eriksson, Huu Le, Michael Milford, Thanh-Toan Do","submitted_at":"2018-10-24T00:11:33Z","abstract_excerpt":"K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a solution with empty clusters. Furthermore, some applications may require the clusters to satisfy a specific set of constraints, e.g., cluster sizes, must-link/cannot-link. Several methods have been introduced to solve constrained K-Means clustering. Due to the non-convex nature of K-Means, however, existing approaches may result in sub-optimal solutions that po"},"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":"1810.10134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-10-24T00:11:33Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a90f4ad6492e80a6ba891b4c0670bc75411508812246da282d5abd3cd59012b2","abstract_canon_sha256":"f7c7b1c1a5b8ad5cbc7177ba5800a5b92c40b48332a416d1e9fd14c302a03f3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:08.729005Z","signature_b64":"T/1DgH+fnHQXto4oidHmoJdtNp75o8J2CPmas+qTrq8aaSR7uqStG1o5Q8XXjfNvIBggm3FyWd/QQjoiCvXIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7bf0a8078b7223e059f80103fbea0525340d59ebb3cafc7dd855a5bb5a77fd0","last_reissued_at":"2026-05-18T00:02:08.728279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:08.728279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Binary Optimization Approach for Constrained K-Means Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Anders Eriksson, Huu Le, Michael Milford, Thanh-Toan Do","submitted_at":"2018-10-24T00:11:33Z","abstract_excerpt":"K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a solution with empty clusters. Furthermore, some applications may require the clusters to satisfy a specific set of constraints, e.g., cluster sizes, must-link/cannot-link. Several methods have been introduced to solve constrained K-Means clustering. Due to the non-convex nature of K-Means, however, existing approaches may result in sub-optimal solutions that po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10134","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":"1810.10134","created_at":"2026-05-18T00:02:08.728413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10134v2","created_at":"2026-05-18T00:02:08.728413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10134","created_at":"2026-05-18T00:02:08.728413+00:00"},{"alias_kind":"pith_short_12","alias_value":"267QVADYW4RD","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"267QVADYW4RD4BM7","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"267QVADY","created_at":"2026-05-18T12:31:59.375834+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/267QVADYW4RD4BM7QAID7PVAKJ","json":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ.json","graph_json":"https://pith.science/api/pith-number/267QVADYW4RD4BM7QAID7PVAKJ/graph.json","events_json":"https://pith.science/api/pith-number/267QVADYW4RD4BM7QAID7PVAKJ/events.json","paper":"https://pith.science/paper/267QVADY"},"agent_actions":{"view_html":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ","download_json":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ.json","view_paper":"https://pith.science/paper/267QVADY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10134&json=true","fetch_graph":"https://pith.science/api/pith-number/267QVADYW4RD4BM7QAID7PVAKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/267QVADYW4RD4BM7QAID7PVAKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ/action/storage_attestation","attest_author":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ/action/author_attestation","sign_citation":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ/action/citation_signature","submit_replication":"https://pith.science/pith/267QVADYW4RD4BM7QAID7PVAKJ/action/replication_record"}},"created_at":"2026-05-18T00:02:08.728413+00:00","updated_at":"2026-05-18T00:02:08.728413+00:00"}