{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6HZ6WHBKAUCBDXZHFLH4TP6ZHV","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":"8621acad6baa86b14283222719e63e73adc61bd777485505b08c8fb7fa2dc095","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-20T12:48:02Z","title_canon_sha256":"becbe6dbc53fe0b4177bf6dc09c85a10dafa60ca3e64f5d9a2e1b87906ea8166"},"schema_version":"1.0","source":{"id":"1802.07091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07091","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07091v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07091","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"6HZ6WHBKAUCB","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6HZ6WHBKAUCBDXZH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6HZ6WHBK","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:0912831829d1b893e7c4fefa875bc9f2e2dd677e4ba36d4a25aa13256f4aa15a","target":"graph","created_at":"2026-05-18T00:22:53Z","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":"Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as clustering path), which is a convex relaxation of hierarchical clustering model, has been proposed in [7] and [5] Although numerical algorithms like ADMM and AMA are proposed to solve convex clustering model [2], it is known to be very challenging to solve large-scale","authors_text":"Defeng Sun, Kim-Chuan Toh, Yancheng Yuan","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-20T12:48:02Z","title":"An Efficient Semismooth Newton Based Algorithm for Convex Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07091","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:e47c81cfcb4f59cca7f858345aa59f9870d76157cd30e289862aa5a7c1eb2fd3","target":"record","created_at":"2026-05-18T00:22:53Z","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":"8621acad6baa86b14283222719e63e73adc61bd777485505b08c8fb7fa2dc095","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-20T12:48:02Z","title_canon_sha256":"becbe6dbc53fe0b4177bf6dc09c85a10dafa60ca3e64f5d9a2e1b87906ea8166"},"schema_version":"1.0","source":{"id":"1802.07091","kind":"arxiv","version":1}},"canonical_sha256":"f1f3eb1c2a050411df272acfc9bfd93d426607bd6a0b096c38e5fb6ca9b8edcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1f3eb1c2a050411df272acfc9bfd93d426607bd6a0b096c38e5fb6ca9b8edcc","first_computed_at":"2026-05-18T00:22:53.574724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:53.574724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K5MCVIiFstlyeVurifWKuvSjbssf+G2nnRQlGI4/UinvjX//ZwdvurAVcl4R47b/7ucl13clyXOLUpWUwMZtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:53.575170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e47c81cfcb4f59cca7f858345aa59f9870d76157cd30e289862aa5a7c1eb2fd3","sha256:0912831829d1b893e7c4fefa875bc9f2e2dd677e4ba36d4a25aa13256f4aa15a"],"state_sha256":"a7f57a01047cebed78bf9e13357b2c665155e8157045b7f0c654690108bbd8b4"}