{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JZRZYF6XGLYTIZVHV4DLUEMAUU","short_pith_number":"pith:JZRZYF6X","canonical_record":{"source":{"id":"1602.01198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-02-03T06:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"e8705b4a417ab8ed2bd39e5f878127e5324093a357148b72d4aaed1ccf0bdee3","abstract_canon_sha256":"eae34999d284716a24f5b75d33ecf3cc3e514926991e9bd901def31926f365b1"},"schema_version":"1.0"},"canonical_sha256":"4e639c17d732f13466a7af06ba1180a53fb4bf37d464418ddc3e5dec213d1977","source":{"kind":"arxiv","id":"1602.01198","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01198","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01198v2","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01198","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"JZRZYF6XGLYT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JZRZYF6XGLYTIZVH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JZRZYF6X","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JZRZYF6XGLYTIZVHV4DLUEMAUU","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-02-03T06:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"e8705b4a417ab8ed2bd39e5f878127e5324093a357148b72d4aaed1ccf0bdee3","abstract_canon_sha256":"eae34999d284716a24f5b75d33ecf3cc3e514926991e9bd901def31926f365b1"},"schema_version":"1.0"},"canonical_sha256":"4e639c17d732f13466a7af06ba1180a53fb4bf37d464418ddc3e5dec213d1977","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:51.643245Z","signature_b64":"qmlBY/rJqfhzRJ8TjyLs0X1S236yxGX6hikBfJxjPKzRNbASrHOT3FwNyn5i9Xn0VMTx5GGVPoxynSCGJGkEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e639c17d732f13466a7af06ba1180a53fb4bf37d464418ddc3e5dec213d1977","last_reissued_at":"2026-05-18T01:20:51.642702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:51.642702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01198","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OqChr/YimGe7R087c3/2iFmGYQUyv6RiyL2AzDOBPlGMYIda31PBpVh8vD5PrNV2efth7vftZrXYODlgGxQeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:27:06.399761Z"},"content_sha256":"84acf2a86c7933ec1fda7380ed039b326bb233097508d16047c6a3efc64f28e2","schema_version":"1.0","event_id":"sha256:84acf2a86c7933ec1fda7380ed039b326bb233097508d16047c6a3efc64f28e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JZRZYF6XGLYTIZVHV4DLUEMAUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"k-variates++: more pluses in the k-means++","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Frank Nielsen, Rapha\\\"el Canyasse, Richard Nock, Roksana Boreli","submitted_at":"2016-02-03T06:31:09Z","abstract_excerpt":"k-means++ seeding has become a de facto standard for hard clustering algorithms. In this paper, our first contribution is a two-way generalisation of this seeding, k-variates++, that includes the sampling of general densities rather than just a discrete set of Dirac densities anchored at the point locations, and a generalisation of the well known Arthur-Vassilvitskii (AV) approximation guarantee, in the form of a bias+variance approximation bound of the global optimum. This approximation exhibits a reduced dependency on the \"noise\" component with respect to the optimal potential --- actually a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01198","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2khwDCJvozyIMixA7kh3lUCQFmaIAtzjhh6q8I4unfL9m2rkPB0SritTNy/G/z/PHIgAeYwY9/VF/QTwqRzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:27:06.400103Z"},"content_sha256":"3c91da31089891cb980d0baf7cca09e1b39d15e3417a7f852d59a18dbca2f730","schema_version":"1.0","event_id":"sha256:3c91da31089891cb980d0baf7cca09e1b39d15e3417a7f852d59a18dbca2f730"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/bundle.json","state_url":"https://pith.science/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T19:27:06Z","links":{"resolver":"https://pith.science/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU","bundle":"https://pith.science/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/bundle.json","state":"https://pith.science/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZRZYF6XGLYTIZVHV4DLUEMAUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JZRZYF6XGLYTIZVHV4DLUEMAUU","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":"eae34999d284716a24f5b75d33ecf3cc3e514926991e9bd901def31926f365b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-02-03T06:31:09Z","title_canon_sha256":"e8705b4a417ab8ed2bd39e5f878127e5324093a357148b72d4aaed1ccf0bdee3"},"schema_version":"1.0","source":{"id":"1602.01198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01198","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01198v2","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01198","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"JZRZYF6XGLYT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JZRZYF6XGLYTIZVH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JZRZYF6X","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:3c91da31089891cb980d0baf7cca09e1b39d15e3417a7f852d59a18dbca2f730","target":"graph","created_at":"2026-05-18T01:20:51Z","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":"k-means++ seeding has become a de facto standard for hard clustering algorithms. In this paper, our first contribution is a two-way generalisation of this seeding, k-variates++, that includes the sampling of general densities rather than just a discrete set of Dirac densities anchored at the point locations, and a generalisation of the well known Arthur-Vassilvitskii (AV) approximation guarantee, in the form of a bias+variance approximation bound of the global optimum. This approximation exhibits a reduced dependency on the \"noise\" component with respect to the optimal potential --- actually a","authors_text":"Frank Nielsen, Rapha\\\"el Canyasse, Richard Nock, Roksana Boreli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-02-03T06:31:09Z","title":"k-variates++: more pluses in the k-means++"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01198","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":"sha256:84acf2a86c7933ec1fda7380ed039b326bb233097508d16047c6a3efc64f28e2","target":"record","created_at":"2026-05-18T01:20:51Z","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":"eae34999d284716a24f5b75d33ecf3cc3e514926991e9bd901def31926f365b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-02-03T06:31:09Z","title_canon_sha256":"e8705b4a417ab8ed2bd39e5f878127e5324093a357148b72d4aaed1ccf0bdee3"},"schema_version":"1.0","source":{"id":"1602.01198","kind":"arxiv","version":2}},"canonical_sha256":"4e639c17d732f13466a7af06ba1180a53fb4bf37d464418ddc3e5dec213d1977","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e639c17d732f13466a7af06ba1180a53fb4bf37d464418ddc3e5dec213d1977","first_computed_at":"2026-05-18T01:20:51.642702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:51.642702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qmlBY/rJqfhzRJ8TjyLs0X1S236yxGX6hikBfJxjPKzRNbASrHOT3FwNyn5i9Xn0VMTx5GGVPoxynSCGJGkEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:51.643245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84acf2a86c7933ec1fda7380ed039b326bb233097508d16047c6a3efc64f28e2","sha256:3c91da31089891cb980d0baf7cca09e1b39d15e3417a7f852d59a18dbca2f730"],"state_sha256":"8e488850aba31567c45107fe7cdca107f6c11fa4a34659f5147886cce9872df5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PotUYmsh1q7TcHX45R+ICpFJ0R/sl3Xq+ajjSjY2UcqklF+JiJVzOwsgf/opsK2JEApen8wHg+7+gp9IB/BBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:27:06.401975Z","bundle_sha256":"d8e3b31a8370335dfa2ab05c4db078d9ec5e567834f09bfbcf62dae823263c99"}}