{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3PR6UO4AGTGNZSAANUDEQ2PSGD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"47d8aadbc90ac9e2c812520b71b2074be3f7aa80252f72a87ce4a411fb64ce24","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-02-09T00:11:27Z","title_canon_sha256":"e78dfa908eae95cd209cf32e36f19f456a803732ac14e3832b0736115b46428a"},"schema_version":"1.0","source":{"id":"1702.02658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02658","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02658v1","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02658","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"3PR6UO4AGTGN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PR6UO4AGTGNZSAA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PR6UO4A","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:e00149403996eacfc404beb751e0f783ef5c14dfd3bedbdac59beb6604e3c73e","target":"graph","created_at":"2026-05-18T00:51:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong modeling assumptions. This paper proposes a data-driven approach to estimate the number of clusters based on a novel form of cross-validation. The proposed method differs from ordinary cross-validation, because clustering is fundamentally an unsupervised learning problem. Simulation and real data analysis results show that the proposed method outperforms existing","authors_text":"Patrick O. Perry, Wei Fu","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-02-09T00:11:27Z","title":"Estimating the number of clusters using cross-validation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02658","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9fa2d00750cf331f36a0ef33caed9dcf7c4b1ceaa27540e2b7a0e4158c67405d","target":"record","created_at":"2026-05-18T00:51:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"47d8aadbc90ac9e2c812520b71b2074be3f7aa80252f72a87ce4a411fb64ce24","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-02-09T00:11:27Z","title_canon_sha256":"e78dfa908eae95cd209cf32e36f19f456a803732ac14e3832b0736115b46428a"},"schema_version":"1.0","source":{"id":"1702.02658","kind":"arxiv","version":1}},"canonical_sha256":"dbe3ea3b8034ccdcc8006d064869f230f66b813d3b91554fa076534d988d6e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe3ea3b8034ccdcc8006d064869f230f66b813d3b91554fa076534d988d6e9a","first_computed_at":"2026-05-18T00:51:03.766750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:03.766750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MEfYjTnsw5LopVqs+3blxT/l4Z3BIRpIddhr8CN5MkxOcm+ey+z/hKeAM+H9MZsD5RfXnGsFqbjqBp50VHxXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:03.767160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fa2d00750cf331f36a0ef33caed9dcf7c4b1ceaa27540e2b7a0e4158c67405d","sha256:e00149403996eacfc404beb751e0f783ef5c14dfd3bedbdac59beb6604e3c73e"],"state_sha256":"9d625bdb5483dbbe38e231186b21e90b4d8b6ce671a75a5d654d30bc0f3b689e"}