{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XUYE4BVUOVO5CUQYAKE5IID7HL","short_pith_number":"pith:XUYE4BVU","schema_version":"1.0","canonical_sha256":"bd304e06b4755dd152180289d4207f3ad929045d4479bd183556a1af76ba53cc","source":{"kind":"arxiv","id":"1610.09269","version":1},"attestation_state":"computed","paper":{"title":"Hierarchical Clustering via Spreading Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aurko Roy, Sebastian Pokutta","submitted_at":"2016-10-28T15:30:21Z","abstract_excerpt":"We study the cost function for hierarchical clusterings introduced by [arXiv:1510.05043] where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters. It was also shown in [arXiv:1510.05043] that a top-down algorithm returns a hierarchical clustering of cost at most $O\\left(\\alpha_n \\log n\\right)$ times the cost of the optimal hierarchical clustering, where $\\alpha_n$ is the approximation ratio of the Sparsest Cut subroutine used. Thus using the best known approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top dow"},"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":"1610.09269","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T15:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"2d71b6b7eff3139a480c99069c0b52e954fbaf292055689fa3e448ddf12106b5","abstract_canon_sha256":"02bf1e29e65e9231a2f3753db25000705cc6bcb0b93afd0973f3a4c870beacc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:58.600028Z","signature_b64":"IPKcOd+9iw0yCRV2CwtT2WTEkEceMrOwRErcqJ7lj1Vguwdv5PDeRI2ahrweyWJMnHfceYhplfRSqR7qN02KCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd304e06b4755dd152180289d4207f3ad929045d4479bd183556a1af76ba53cc","last_reissued_at":"2026-05-18T01:00:58.599527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:58.599527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Clustering via Spreading Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aurko Roy, Sebastian Pokutta","submitted_at":"2016-10-28T15:30:21Z","abstract_excerpt":"We study the cost function for hierarchical clusterings introduced by [arXiv:1510.05043] where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters. It was also shown in [arXiv:1510.05043] that a top-down algorithm returns a hierarchical clustering of cost at most $O\\left(\\alpha_n \\log n\\right)$ times the cost of the optimal hierarchical clustering, where $\\alpha_n$ is the approximation ratio of the Sparsest Cut subroutine used. Thus using the best known approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top dow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09269","kind":"arxiv","version":1},"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":"1610.09269","created_at":"2026-05-18T01:00:58.599606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09269v1","created_at":"2026-05-18T01:00:58.599606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09269","created_at":"2026-05-18T01:00:58.599606+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUYE4BVUOVO5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUYE4BVUOVO5CUQY","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUYE4BVU","created_at":"2026-05-18T12:30:51.357362+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/XUYE4BVUOVO5CUQYAKE5IID7HL","json":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL.json","graph_json":"https://pith.science/api/pith-number/XUYE4BVUOVO5CUQYAKE5IID7HL/graph.json","events_json":"https://pith.science/api/pith-number/XUYE4BVUOVO5CUQYAKE5IID7HL/events.json","paper":"https://pith.science/paper/XUYE4BVU"},"agent_actions":{"view_html":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL","download_json":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL.json","view_paper":"https://pith.science/paper/XUYE4BVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09269&json=true","fetch_graph":"https://pith.science/api/pith-number/XUYE4BVUOVO5CUQYAKE5IID7HL/graph.json","fetch_events":"https://pith.science/api/pith-number/XUYE4BVUOVO5CUQYAKE5IID7HL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL/action/storage_attestation","attest_author":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL/action/author_attestation","sign_citation":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL/action/citation_signature","submit_replication":"https://pith.science/pith/XUYE4BVUOVO5CUQYAKE5IID7HL/action/replication_record"}},"created_at":"2026-05-18T01:00:58.599606+00:00","updated_at":"2026-05-18T01:00:58.599606+00:00"}