{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ESNRLB2ENHH3WQNLAPZFMEGJYK","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":"91b6f765484a7229375434f67569c73391d23c908cfa1d2e43a7a5a2b81d8643","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-08-21T11:31:04Z","title_canon_sha256":"f1dcd9b81fc4fc9cb208f5168e14253f0fb60d46d8a87f229e79ef48e53a6a1e"},"schema_version":"1.0","source":{"id":"1508.05243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05243","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05243v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05243","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"ESNRLB2ENHH3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ESNRLB2ENHH3WQNL","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ESNRLB2E","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:c10ee19f8933043807906b526a45d00e082b92e5a55f427650c355f08c1a12bd","target":"graph","created_at":"2026-05-18T01:15:58Z","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":"Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now, the algorithms and the corresponding theory were usually specific to each clustering problem.\n  We propose a single, practical algorithm to construct strong coresets for a large class of hard and soft clustering problems based on Bregman divergences. This class includes hard clu","authors_text":"Andreas Krause, Mario Lucic, Olivier Bachem","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-08-21T11:31:04Z","title":"Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05243","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":"sha256:64307d4af227dfe7b311b396aed73e30ea7ae06ca190fad9092df06b5f83da03","target":"record","created_at":"2026-05-18T01:15:58Z","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":"91b6f765484a7229375434f67569c73391d23c908cfa1d2e43a7a5a2b81d8643","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-08-21T11:31:04Z","title_canon_sha256":"f1dcd9b81fc4fc9cb208f5168e14253f0fb60d46d8a87f229e79ef48e53a6a1e"},"schema_version":"1.0","source":{"id":"1508.05243","kind":"arxiv","version":2}},"canonical_sha256":"249b15874469cfbb41ab03f25610c9c291743d0cf63254345d6aca1f9c989fa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"249b15874469cfbb41ab03f25610c9c291743d0cf63254345d6aca1f9c989fa2","first_computed_at":"2026-05-18T01:15:58.328347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:58.328347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zzMOch9gzby98XRxnfGIUJ5gtrUkQgExoAVHDB423adsMNNWwxQ0f6AqtOPlZF/xlZssBmhu9B1qdqBmDyaXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:58.329043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64307d4af227dfe7b311b396aed73e30ea7ae06ca190fad9092df06b5f83da03","sha256:c10ee19f8933043807906b526a45d00e082b92e5a55f427650c355f08c1a12bd"],"state_sha256":"4bb82a1b39a4bf6642f50e011455baf8a3651d54d7f79c8cbf0c17f107805a55"}