{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TMYRIVUUW7RHXJK67C7CG7SQZG","short_pith_number":"pith:TMYRIVUU","canonical_record":{"source":{"id":"2506.02053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-06-01T09:34:52Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"4ea2de425d2747b9af01bd15154901e5f6a8c06d2d15aa29592003c4faee0e4b","abstract_canon_sha256":"0499d1ccbfcb926876d7021749959363cc8c3f37d59bd4880f8684ce95302934"},"schema_version":"1.0"},"canonical_sha256":"9b31145694b7e27ba55ef8be237e50c9bacfbd4b954de65a07c8cde540313832","source":{"kind":"arxiv","id":"2506.02053","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02053","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02053v1","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02053","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_12","alias_value":"TMYRIVUUW7RH","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_16","alias_value":"TMYRIVUUW7RHXJK6","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_8","alias_value":"TMYRIVUU","created_at":"2026-07-05T11:14:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TMYRIVUUW7RHXJK67C7CG7SQZG","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-06-01T09:34:52Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"4ea2de425d2747b9af01bd15154901e5f6a8c06d2d15aa29592003c4faee0e4b","abstract_canon_sha256":"0499d1ccbfcb926876d7021749959363cc8c3f37d59bd4880f8684ce95302934"},"schema_version":"1.0"},"canonical_sha256":"9b31145694b7e27ba55ef8be237e50c9bacfbd4b954de65a07c8cde540313832","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:31.499921Z","signature_b64":"KxwMHRTA3Znow7Ymazb80IbRDoGlagV1IgMlO+KX8MJE0IUxiRJVgAmMglA7mFlhhmTCrQsdTAc8Qhch/uEOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b31145694b7e27ba55ef8be237e50c9bacfbd4b954de65a07c8cde540313832","last_reissued_at":"2026-07-05T11:14:31.499520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:31.499520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02053","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:14:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSKixVDvr38itfmRmx+55EmYe1wdTDt0JF/1a6zscc1ohFE4AEPYKj6+bRM7cAbg/65Qf93FVu75lKlfRs/8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:35:14.158043Z"},"content_sha256":"c80b96db1311f53d59e10dd1741b86c2db43a468f2e8d51383850bd2d1ea818c","schema_version":"1.0","event_id":"sha256:c80b96db1311f53d59e10dd1741b86c2db43a468f2e8d51383850bd2d1ea818c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TMYRIVUUW7RHXJK67C7CG7SQZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization Performance of Ensemble Clustering: From Theory to Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Haoye Qiu, Hui Liu, Junhui Hou, Weixuan Liang, Xu Zhang, Yuheng Jia","submitted_at":"2025-06-01T09:34:52Z","abstract_excerpt":"Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess risk and consistency. We derive a convergence rate of generalization error bound and excess risk bound both of $\\mathcal{O}(\\sqrt{\\frac{\\log n}{m}}+\\frac{1}{\\sqrt{n}})$, with $n$ and $m$ being the numbers of samples and base clusterings. Based on this, we prove that when $m$ and $n$ approach infinity and $m$ is significantly larger than log $n$, i.e., $m,n\\to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:14:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BuCwfYkmm6aH+JsT+xWzk9VcI4bc4oLDcBHGeuiATacfZZZfd3K3HealYxIpr0U0rEOrhladYF78iG5U42dUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:35:14.158776Z"},"content_sha256":"53b7d795983835fa319fc765a81210acf64d14f3f6fc7dae605ae631587b935a","schema_version":"1.0","event_id":"sha256:53b7d795983835fa319fc765a81210acf64d14f3f6fc7dae605ae631587b935a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/bundle.json","state_url":"https://pith.science/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/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":"2026-08-06T09:35:14Z","links":{"resolver":"https://pith.science/pith/TMYRIVUUW7RHXJK67C7CG7SQZG","bundle":"https://pith.science/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/bundle.json","state":"https://pith.science/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMYRIVUUW7RHXJK67C7CG7SQZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TMYRIVUUW7RHXJK67C7CG7SQZG","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":"0499d1ccbfcb926876d7021749959363cc8c3f37d59bd4880f8684ce95302934","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-06-01T09:34:52Z","title_canon_sha256":"4ea2de425d2747b9af01bd15154901e5f6a8c06d2d15aa29592003c4faee0e4b"},"schema_version":"1.0","source":{"id":"2506.02053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02053","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02053v1","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02053","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_12","alias_value":"TMYRIVUUW7RH","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_16","alias_value":"TMYRIVUUW7RHXJK6","created_at":"2026-07-05T11:14:31Z"},{"alias_kind":"pith_short_8","alias_value":"TMYRIVUU","created_at":"2026-07-05T11:14:31Z"}],"graph_snapshots":[{"event_id":"sha256:53b7d795983835fa319fc765a81210acf64d14f3f6fc7dae605ae631587b935a","target":"graph","created_at":"2026-07-05T11:14:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess risk and consistency. We derive a convergence rate of generalization error bound and excess risk bound both of $\\mathcal{O}(\\sqrt{\\frac{\\log n}{m}}+\\frac{1}{\\sqrt{n}})$, with $n$ and $m$ being the numbers of samples and base clusterings. Based on this, we prove that when $m$ and $n$ approach infinity and $m$ is significantly larger than log $n$, i.e., $m,n\\to","authors_text":"Haoye Qiu, Hui Liu, Junhui Hou, Weixuan Liang, Xu Zhang, Yuheng Jia","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-06-01T09:34:52Z","title":"Generalization Performance of Ensemble Clustering: From Theory to Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02053","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:c80b96db1311f53d59e10dd1741b86c2db43a468f2e8d51383850bd2d1ea818c","target":"record","created_at":"2026-07-05T11:14:31Z","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":"0499d1ccbfcb926876d7021749959363cc8c3f37d59bd4880f8684ce95302934","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-06-01T09:34:52Z","title_canon_sha256":"4ea2de425d2747b9af01bd15154901e5f6a8c06d2d15aa29592003c4faee0e4b"},"schema_version":"1.0","source":{"id":"2506.02053","kind":"arxiv","version":1}},"canonical_sha256":"9b31145694b7e27ba55ef8be237e50c9bacfbd4b954de65a07c8cde540313832","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b31145694b7e27ba55ef8be237e50c9bacfbd4b954de65a07c8cde540313832","first_computed_at":"2026-07-05T11:14:31.499520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:31.499520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KxwMHRTA3Znow7Ymazb80IbRDoGlagV1IgMlO+KX8MJE0IUxiRJVgAmMglA7mFlhhmTCrQsdTAc8Qhch/uEOCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:31.499921Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c80b96db1311f53d59e10dd1741b86c2db43a468f2e8d51383850bd2d1ea818c","sha256:53b7d795983835fa319fc765a81210acf64d14f3f6fc7dae605ae631587b935a"],"state_sha256":"fc636825c07540bd80746a1eaa7d4095f179fed236eedf85f81bb9e025885c25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gk6ROi5ZGC9vK3XJtLTDLmR4khrNfUEeybiW87VlN6Ai7GlFIhjJ8sBrdtucfty/6Z6bddu9d/8SkgavN52tDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T09:35:14.164541Z","bundle_sha256":"5106b4486686f3aefae0b2b28e64cead50e4009ba1981374a763051775708700"}}