{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QEM5KXPIYUNPSMLUGQV45L62SH","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":"2f664641dee13c2d7a2c6b64c3ba779f520ac326f197343cc40b6d0b4a98ec7d","cross_cats_sorted":["cs.CG","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-01-31T22:21:19Z","title_canon_sha256":"0df985f3ad7e25761972895a145e4f36a598b3ce841aab35b85e41048612f686"},"schema_version":"1.0","source":{"id":"1102.0026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0026","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0026v1","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0026","created_at":"2026-05-18T02:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"QEM5KXPIYUNP","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QEM5KXPIYUNPSMLU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QEM5KXPI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:6bce10ca74ab460e045067cfb562d66b0c2a26332a407d5a0e427ebaee15c19a","target":"graph","created_at":"2026-05-18T02:22:41Z","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":"This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a combination of the representations of their constituent points. We use this representation and the underlying metric to design a spatially-aware consensus clustering procedure. This consensus procedure is implemented via a novel reduction to Euclidean clustering, and is both simple and efficient. All of our results apply to both soft and hard clusterings. We acc","authors_text":"Jeff M. Phillips, Parasaran Raman, Suresh Venkatasubramanian","cross_cats":["cs.CG","cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-01-31T22:21:19Z","title":"Spatially-Aware Comparison and Consensus for Clusterings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0026","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":"sha256:40db902b47517e2d16c9674fecd4b0c628e26f77b6e81e775c3dee712dcccfac","target":"record","created_at":"2026-05-18T02:22:41Z","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":"2f664641dee13c2d7a2c6b64c3ba779f520ac326f197343cc40b6d0b4a98ec7d","cross_cats_sorted":["cs.CG","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-01-31T22:21:19Z","title_canon_sha256":"0df985f3ad7e25761972895a145e4f36a598b3ce841aab35b85e41048612f686"},"schema_version":"1.0","source":{"id":"1102.0026","kind":"arxiv","version":1}},"canonical_sha256":"8119d55de8c51af93174342bceafda91e30df628a8fd5a8f694963fcdbea3b40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8119d55de8c51af93174342bceafda91e30df628a8fd5a8f694963fcdbea3b40","first_computed_at":"2026-05-18T02:22:41.577089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:41.577089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTBesSaVUh9CpMIMWDAuojwCqwUyk/Yu+kCuvX1Ca04DYHvBwlUTVDGioSeU1ppbnZLnWXc6TXw2IaR+GuhWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:41.577791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40db902b47517e2d16c9674fecd4b0c628e26f77b6e81e775c3dee712dcccfac","sha256:6bce10ca74ab460e045067cfb562d66b0c2a26332a407d5a0e427ebaee15c19a"],"state_sha256":"b4572b0854106dab3137ca1f68154c18c504455b718e2d31f864033caef498a0"}