{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FOCU6EQJXMSS67R7KXTLB4HBG2","short_pith_number":"pith:FOCU6EQJ","schema_version":"1.0","canonical_sha256":"2b854f1209bb252f7e3f55e6b0f0e136829972f4eac95af96fd6ddb14669a7eb","source":{"kind":"arxiv","id":"1412.0753","version":5},"attestation_state":"computed","paper":{"title":"Convex clustering via $\\ell_1$ fusion penalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Gourab Mukherjee, Peter Radchenko","submitted_at":"2014-12-02T01:10:11Z","abstract_excerpt":"We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in popularity, however, its asymptotic properties have remained mostly unknown. Our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems. We use this representation to provide a simple and intuitive formulation for the population clustering procedure. We "},"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":"1412.0753","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-12-02T01:10:11Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"f8dcf96e95251c463766fddd1c71394eb622340fa94738eddc1f326c05347d70","abstract_canon_sha256":"ba1a6d70ec0e9a6410fbf8f297b2bff1ebca485965f9f7215fe19e9f78e172e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:51.444921Z","signature_b64":"6DUJ3rJyuhhfcBMcyjE1qWLpR3P+3oQ0NAOXf2BaUDDuucv3UyylS8JhPeoksmxMIz79EkDfxhiJZVGzsku/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b854f1209bb252f7e3f55e6b0f0e136829972f4eac95af96fd6ddb14669a7eb","last_reissued_at":"2026-05-18T00:53:51.444486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:51.444486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex clustering via $\\ell_1$ fusion penalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Gourab Mukherjee, Peter Radchenko","submitted_at":"2014-12-02T01:10:11Z","abstract_excerpt":"We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in popularity, however, its asymptotic properties have remained mostly unknown. Our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems. We use this representation to provide a simple and intuitive formulation for the population clustering procedure. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0753","kind":"arxiv","version":5},"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":"1412.0753","created_at":"2026-05-18T00:53:51.444562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0753v5","created_at":"2026-05-18T00:53:51.444562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0753","created_at":"2026-05-18T00:53:51.444562+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOCU6EQJXMSS","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOCU6EQJXMSS67R7","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOCU6EQJ","created_at":"2026-05-18T12:28:28.263976+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/FOCU6EQJXMSS67R7KXTLB4HBG2","json":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2.json","graph_json":"https://pith.science/api/pith-number/FOCU6EQJXMSS67R7KXTLB4HBG2/graph.json","events_json":"https://pith.science/api/pith-number/FOCU6EQJXMSS67R7KXTLB4HBG2/events.json","paper":"https://pith.science/paper/FOCU6EQJ"},"agent_actions":{"view_html":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2","download_json":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2.json","view_paper":"https://pith.science/paper/FOCU6EQJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0753&json=true","fetch_graph":"https://pith.science/api/pith-number/FOCU6EQJXMSS67R7KXTLB4HBG2/graph.json","fetch_events":"https://pith.science/api/pith-number/FOCU6EQJXMSS67R7KXTLB4HBG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2/action/storage_attestation","attest_author":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2/action/author_attestation","sign_citation":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2/action/citation_signature","submit_replication":"https://pith.science/pith/FOCU6EQJXMSS67R7KXTLB4HBG2/action/replication_record"}},"created_at":"2026-05-18T00:53:51.444562+00:00","updated_at":"2026-05-18T00:53:51.444562+00:00"}