{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DJIWNL24JLTC5Q3NEVQ4UNYGAZ","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":"ea1336ca139cf543fe05a25a8b1ba23b39ac431b5a8d5b4d4c89f245e0e2fb6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-11-12T21:18:12Z","title_canon_sha256":"4e46a86cf43d8201564fdbae6c1ac8ac1de49c4d342c81ce73edf875e1ff2147"},"schema_version":"1.0","source":{"id":"1711.04359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04359","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04359v1","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04359","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"DJIWNL24JLTC","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJIWNL24JLTC5Q3N","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJIWNL24","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:28865c1b80ec5dad109010e1036f0db232a356a241e765b511c7f0f51af9021e","target":"graph","created_at":"2026-05-18T00:30:39Z","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 propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns observations to clusters according to a multi-sample energy statistic that measures the distance between distributions. The energy distance determines a consistent test for equality of distributions, and it is based on a population distance that characterizes equality of distributions. The k-groups procedure therefore generalizes the k-means method, which separates clusters that have different means. We propose two k-gro","authors_text":"Maria L. Rizzo, Songzi Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-11-12T21:18:12Z","title":"K-groups: A Generalization of K-means Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04359","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":"sha256:97e8079245577c79537a1977b837acc0435e8369be26bfa02d4fa96ef58a0f4b","target":"record","created_at":"2026-05-18T00:30:39Z","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":"ea1336ca139cf543fe05a25a8b1ba23b39ac431b5a8d5b4d4c89f245e0e2fb6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-11-12T21:18:12Z","title_canon_sha256":"4e46a86cf43d8201564fdbae6c1ac8ac1de49c4d342c81ce73edf875e1ff2147"},"schema_version":"1.0","source":{"id":"1711.04359","kind":"arxiv","version":1}},"canonical_sha256":"1a5166af5c4ae62ec36d2561ca37060676f9116fda8e2d5632288ba8a65a9748","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a5166af5c4ae62ec36d2561ca37060676f9116fda8e2d5632288ba8a65a9748","first_computed_at":"2026-05-18T00:30:39.271539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:39.271539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5q4tHOmB3zvaGWPP/Ua7ybb9i60dUrTR4ZhQrlwQSssNC+o4JolqKnKU+sXu//oAP2Hf3WAOPON/4nOjXmXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:39.272235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97e8079245577c79537a1977b837acc0435e8369be26bfa02d4fa96ef58a0f4b","sha256:28865c1b80ec5dad109010e1036f0db232a356a241e765b511c7f0f51af9021e"],"state_sha256":"fbb5a175c1daa951af6969db12b1540eab262c2ace7e8b2714d3e64497528376"}