{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NN2JHGUQUKNWO64WWF67T5MAMS","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":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e"},"schema_version":"1.0","source":{"id":"2108.06036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2108.06036v1","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"NN2JHGUQUKNW","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"NN2JHGUQUKNWO64W","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"NN2JHGUQ","created_at":"2026-07-05T03:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497","target":"graph","created_at":"2026-07-05T03:05:36Z","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/2108.06036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A combinatorial cost function for hierarchical clustering was introduced by Dasgupta \\cite{dasgupta2016cost}. It has been generalized by Cohen-Addad et al. \\cite{cohen2019hierarchical} to a general form named admissible function. In this paper, we investigate hierarchical clustering from the \\emph{information-theoretic} perspective and formulate a new objective function. We also establish the relationship between these two perspectives. In algorithmic aspect, we get rid of the traditional top-down and bottom-up frameworks, and propose a new one to stratify the \\emph{sparsest} level of a cluste","authors_text":"Bingchen Fan, Feng Zheng, Yicheng Pan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title":"An Information-theoretic Perspective of Hierarchical Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06036","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":"sha256:2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7","target":"record","created_at":"2026-07-05T03:05:36Z","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":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e"},"schema_version":"1.0","source":{"id":"2108.06036","kind":"arxiv","version":1}},"canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","first_computed_at":"2026-07-05T03:05:36.900544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:05:36.900544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0rHhWG0n094BbH7FWg0/oZAe919SPvTsWbNP7PMFLzCCrRH249UV6gRHtCjzGF1A+ydGsTK3zMsVmTOT11UyBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:05:36.900922Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.06036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7","sha256:97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497"],"state_sha256":"db3a9a5f25d631784d7aa10c98e277f7a425ed04507ec2598328105d1de65f26"}