{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ST2ZWT6EBC3LZB5HJAM66PCHJE","short_pith_number":"pith:ST2ZWT6E","canonical_record":{"source":{"id":"1503.08340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-03-28T19:47:51Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"d247ecbb55d2b5c65a1a486f3c71cafda734d1a3513bb198ea48a665e7d383e3","abstract_canon_sha256":"3a188dcbcbb1dc63e047401cfbd4c241f6dd7a52bdf2f56b835e011d315c1696"},"schema_version":"1.0"},"canonical_sha256":"94f59b4fc408b6bc87a74819ef3c47490c94babef4b946fe6967dcab8911c609","source":{"kind":"arxiv","id":"1503.08340","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08340","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08340v2","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08340","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"pith_short_12","alias_value":"ST2ZWT6EBC3L","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"ST2ZWT6EBC3LZB5H","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"ST2ZWT6E","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ST2ZWT6EBC3LZB5HJAM66PCHJE","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-03-28T19:47:51Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"d247ecbb55d2b5c65a1a486f3c71cafda734d1a3513bb198ea48a665e7d383e3","abstract_canon_sha256":"3a188dcbcbb1dc63e047401cfbd4c241f6dd7a52bdf2f56b835e011d315c1696"},"schema_version":"1.0"},"canonical_sha256":"94f59b4fc408b6bc87a74819ef3c47490c94babef4b946fe6967dcab8911c609","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:15.939225Z","signature_b64":"SSn4OgcuyQdzCempK/q3rBume9QFPMIVqzBT0e8cGhNC/aMxdRFd+6g7hR8jzTu2byBjqjkb+yOVmcu1VCSQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94f59b4fc408b6bc87a74819ef3c47490c94babef4b946fe6967dcab8911c609","last_reissued_at":"2026-05-18T01:33:15.938567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:15.938567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08340","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+EOTq+O15kvEEb4UXS0VUJBbC0cLKQGc7MWQYrRxzwo3zbCDurEhkQc0YaxnyMbf4Tw/S6amUaI2e2Rg1zrwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T00:54:18.728548Z"},"content_sha256":"ae35d2e4fdf45a366d9af6018681d34855e724250bf540604d74f03371c6f671","schema_version":"1.0","event_id":"sha256:ae35d2e4fdf45a366d9af6018681d34855e724250bf540604d74f03371c6f671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ST2ZWT6EBC3LZB5HJAM66PCHJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Properties of Convex Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Daniela Witten, Kean Ming Tan","submitted_at":"2015-03-28T19:47:51Z","abstract_excerpt":"In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimate of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in simulation studies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08340","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2AnlNoKHGDco5IEJF2g50fPBKgCtOXDSDEeKxuo4mqWhwky++rpWv03CxbVHoVBR9SE61Q/XcNQFujIyHY+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T00:54:18.729233Z"},"content_sha256":"25444a4a268ae34ccc2492d511b47c3345ca58833199129c56ea58cdaccd84c2","schema_version":"1.0","event_id":"sha256:25444a4a268ae34ccc2492d511b47c3345ca58833199129c56ea58cdaccd84c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/bundle.json","state_url":"https://pith.science/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T00:54:18Z","links":{"resolver":"https://pith.science/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE","bundle":"https://pith.science/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/bundle.json","state":"https://pith.science/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ST2ZWT6EBC3LZB5HJAM66PCHJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ST2ZWT6EBC3LZB5HJAM66PCHJE","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":"3a188dcbcbb1dc63e047401cfbd4c241f6dd7a52bdf2f56b835e011d315c1696","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-03-28T19:47:51Z","title_canon_sha256":"d247ecbb55d2b5c65a1a486f3c71cafda734d1a3513bb198ea48a665e7d383e3"},"schema_version":"1.0","source":{"id":"1503.08340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08340","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08340v2","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08340","created_at":"2026-05-18T01:33:15Z"},{"alias_kind":"pith_short_12","alias_value":"ST2ZWT6EBC3L","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"ST2ZWT6EBC3LZB5H","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"ST2ZWT6E","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:25444a4a268ae34ccc2492d511b47c3345ca58833199129c56ea58cdaccd84c2","target":"graph","created_at":"2026-05-18T01:33:15Z","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":"In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimate of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in simulation studies.","authors_text":"Daniela Witten, Kean Ming Tan","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-03-28T19:47:51Z","title":"Statistical Properties of Convex Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08340","kind":"arxiv","version":2},"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:ae35d2e4fdf45a366d9af6018681d34855e724250bf540604d74f03371c6f671","target":"record","created_at":"2026-05-18T01:33:15Z","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":"3a188dcbcbb1dc63e047401cfbd4c241f6dd7a52bdf2f56b835e011d315c1696","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-03-28T19:47:51Z","title_canon_sha256":"d247ecbb55d2b5c65a1a486f3c71cafda734d1a3513bb198ea48a665e7d383e3"},"schema_version":"1.0","source":{"id":"1503.08340","kind":"arxiv","version":2}},"canonical_sha256":"94f59b4fc408b6bc87a74819ef3c47490c94babef4b946fe6967dcab8911c609","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94f59b4fc408b6bc87a74819ef3c47490c94babef4b946fe6967dcab8911c609","first_computed_at":"2026-05-18T01:33:15.938567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:15.938567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSn4OgcuyQdzCempK/q3rBume9QFPMIVqzBT0e8cGhNC/aMxdRFd+6g7hR8jzTu2byBjqjkb+yOVmcu1VCSQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:15.939225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae35d2e4fdf45a366d9af6018681d34855e724250bf540604d74f03371c6f671","sha256:25444a4a268ae34ccc2492d511b47c3345ca58833199129c56ea58cdaccd84c2"],"state_sha256":"153434db9829f3fa83e8e00ed5fa622598d4341a330ba94c151a793db497dd1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AQ0z8q87cKIQrlnIng4DTZ4fUIGdvT+qWCasH2IRPyExRSWSm4oaOK5Q5pbbx0KMv5aN/Q5SeTDYPqCQXsvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T00:54:18.732457Z","bundle_sha256":"7cb46f5168efbb8880c8a3d284ccf5c373d3e3b5b5b10babdae7917c7a7fbb05"}}