{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SPK2JFWG7RJXK4M2N4MCUG6GXR","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":"8e52ba280a8336ef0bc7ff9f7afccd1d51abafc53e66bc59977c98ad32fd5126","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-15T13:04:13Z","title_canon_sha256":"6700af9f98f0444ab43f2918561c097465b7dcb6043f7c81fe1ea88c15eb623e"},"schema_version":"1.0","source":{"id":"1806.05938","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05938","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05938v2","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05938","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"SPK2JFWG7RJX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SPK2JFWG7RJXK4M2","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SPK2JFWG","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:3fdc544586804401412a2b7c3d126d38afcf933fa785b4abfc786296f5fc902a","target":"graph","created_at":"2026-05-18T00:01:09Z","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":"We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size, one can obtain an $(1+\\epsilon)$-approximation for the optimal potential with probability at least $1-\\delta$, where $\\epsilon>0$ and $\\delta\\in(0,1)$, using an expected number of $O(\\frac{K^3}{\\epsilon \\delta})$ noiseless same-cluster queries and comparison-based clustering of complexity $O(ndK + \\frac{K^3}{\\epsilon \\delta})$, here, $n$ denotes the number of","authors_text":"Chao Pan, I Chien, Olgica Milenkovic","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-15T13:04:13Z","title":"Query K-means Clustering and the Double Dixie Cup Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05938","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":"sha256:456089d0ea1c6ede863b4c30f5ac34e028b66afa3f4db4febf9e8205edb02c31","target":"record","created_at":"2026-05-18T00:01:09Z","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":"8e52ba280a8336ef0bc7ff9f7afccd1d51abafc53e66bc59977c98ad32fd5126","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-15T13:04:13Z","title_canon_sha256":"6700af9f98f0444ab43f2918561c097465b7dcb6043f7c81fe1ea88c15eb623e"},"schema_version":"1.0","source":{"id":"1806.05938","kind":"arxiv","version":2}},"canonical_sha256":"93d5a496c6fc5375719a6f182a1bc6bc48af4c48102e479cf6324dd2b9e3ff81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93d5a496c6fc5375719a6f182a1bc6bc48af4c48102e479cf6324dd2b9e3ff81","first_computed_at":"2026-05-18T00:01:09.228581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:09.228581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mV0h52AhFIVdMW/EATAl3Y3K/bkxkejGoId+2qS4Op8uqysuCy3boY3HEtU40io66yhIXysZRJCG+2reP6pXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:09.229194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05938","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:456089d0ea1c6ede863b4c30f5ac34e028b66afa3f4db4febf9e8205edb02c31","sha256:3fdc544586804401412a2b7c3d126d38afcf933fa785b4abfc786296f5fc902a"],"state_sha256":"458cf512957baf713f868f24c4ed5f17c1548257625190a21731288e7eb0d48d"}