{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DX7URYOFZZ4QSXC5XAY7BF23UY","short_pith_number":"pith:DX7URYOF","schema_version":"1.0","canonical_sha256":"1dff48e1c5ce79095c5db831f0975ba60ede181ef639e1c7e265139289cb282d","source":{"kind":"arxiv","id":"1510.00012","version":4},"attestation_state":"computed","paper":{"title":"Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"stat.CO","authors_text":"James Z. Wang, Jia Li, Jianbo Ye, Panruo Wu","submitted_at":"2015-09-30T20:10:59Z","abstract_excerpt":"In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metric. D2-clustering has a severe scalability issue, the bottleneck being the computation of a centroid distribution, called Wasserstein barycenter, that minimizes its sum of squared distances to the cluster members. In this paper, we develop a modified Bregman ADMM approach for com"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.00012","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-09-30T20:10:59Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"8fccc940c05cf1b1262880005d0b8f1ce050c9c6245679b767fd89dca768ff34","abstract_canon_sha256":"b17910c5bcef06ac4a5e225f09fcf4f4bc2d8047fb3a2507a9183e6d660860a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.535903Z","signature_b64":"vSrcQALIAME5lsmA0h8DAYQ1WdPdZck4snYEMZYnAT9y1Vip3hd4YByKa2JbO8kjD8D/zGE4198Be0obxxzODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dff48e1c5ce79095c5db831f0975ba60ede181ef639e1c7e265139289cb282d","last_reissued_at":"2026-05-18T00:53:12.535488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.535488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"stat.CO","authors_text":"James Z. Wang, Jia Li, Jianbo Ye, Panruo Wu","submitted_at":"2015-09-30T20:10:59Z","abstract_excerpt":"In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metric. D2-clustering has a severe scalability issue, the bottleneck being the computation of a centroid distribution, called Wasserstein barycenter, that minimizes its sum of squared distances to the cluster members. In this paper, we develop a modified Bregman ADMM approach for com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00012","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.00012","created_at":"2026-05-18T00:53:12.535559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00012v4","created_at":"2026-05-18T00:53:12.535559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00012","created_at":"2026-05-18T00:53:12.535559+00:00"},{"alias_kind":"pith_short_12","alias_value":"DX7URYOFZZ4Q","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DX7URYOFZZ4QSXC5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DX7URYOF","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY","json":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY.json","graph_json":"https://pith.science/api/pith-number/DX7URYOFZZ4QSXC5XAY7BF23UY/graph.json","events_json":"https://pith.science/api/pith-number/DX7URYOFZZ4QSXC5XAY7BF23UY/events.json","paper":"https://pith.science/paper/DX7URYOF"},"agent_actions":{"view_html":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY","download_json":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY.json","view_paper":"https://pith.science/paper/DX7URYOF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00012&json=true","fetch_graph":"https://pith.science/api/pith-number/DX7URYOFZZ4QSXC5XAY7BF23UY/graph.json","fetch_events":"https://pith.science/api/pith-number/DX7URYOFZZ4QSXC5XAY7BF23UY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY/action/storage_attestation","attest_author":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY/action/author_attestation","sign_citation":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY/action/citation_signature","submit_replication":"https://pith.science/pith/DX7URYOFZZ4QSXC5XAY7BF23UY/action/replication_record"}},"created_at":"2026-05-18T00:53:12.535559+00:00","updated_at":"2026-05-18T00:53:12.535559+00:00"}