{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G3QEPXLLRF6FJYLCXHZOHG5XMO","short_pith_number":"pith:G3QEPXLL","schema_version":"1.0","canonical_sha256":"36e047dd6b897c54e162b9f2e39bb763bd94fa47370bd0d27f22cb8e62340d54","source":{"kind":"arxiv","id":"1511.09153","version":1},"attestation_state":"computed","paper":{"title":"Alternating direction method of multipliers for regularized multiclass support vector machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Amit Chakraborty, Ioannis Akrotirianakis, Yangyang Xu","submitted_at":"2015-11-30T04:47:50Z","abstract_excerpt":"The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to th"},"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":"1511.09153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T04:47:50Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6798a506daa06033d18dfdb8b0c7fb44086f4623942a2d97ecfadd1af7cfec16","abstract_canon_sha256":"c4f67f44bb030c3c3149a3f47fd7dc886feee4588ece4aad0b77dbc753a6a955"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:40.950352Z","signature_b64":"JpI3mCG/Dljfno/2ciFQrGPJ5fHwVJdoZPMQRqLmhY5BQGxl75Vr2bqdeJ8ehcuzxqOMfDYYhoaM2pz9ggioBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36e047dd6b897c54e162b9f2e39bb763bd94fa47370bd0d27f22cb8e62340d54","last_reissued_at":"2026-05-18T01:25:40.949714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:40.949714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alternating direction method of multipliers for regularized multiclass support vector machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Amit Chakraborty, Ioannis Akrotirianakis, Yangyang Xu","submitted_at":"2015-11-30T04:47:50Z","abstract_excerpt":"The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09153","kind":"arxiv","version":1},"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":"1511.09153","created_at":"2026-05-18T01:25:40.949829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.09153v1","created_at":"2026-05-18T01:25:40.949829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09153","created_at":"2026-05-18T01:25:40.949829+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3QEPXLLRF6F","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3QEPXLLRF6FJYLC","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3QEPXLL","created_at":"2026-05-18T12:29:22.688609+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/G3QEPXLLRF6FJYLCXHZOHG5XMO","json":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO.json","graph_json":"https://pith.science/api/pith-number/G3QEPXLLRF6FJYLCXHZOHG5XMO/graph.json","events_json":"https://pith.science/api/pith-number/G3QEPXLLRF6FJYLCXHZOHG5XMO/events.json","paper":"https://pith.science/paper/G3QEPXLL"},"agent_actions":{"view_html":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO","download_json":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO.json","view_paper":"https://pith.science/paper/G3QEPXLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.09153&json=true","fetch_graph":"https://pith.science/api/pith-number/G3QEPXLLRF6FJYLCXHZOHG5XMO/graph.json","fetch_events":"https://pith.science/api/pith-number/G3QEPXLLRF6FJYLCXHZOHG5XMO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO/action/storage_attestation","attest_author":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO/action/author_attestation","sign_citation":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO/action/citation_signature","submit_replication":"https://pith.science/pith/G3QEPXLLRF6FJYLCXHZOHG5XMO/action/replication_record"}},"created_at":"2026-05-18T01:25:40.949829+00:00","updated_at":"2026-05-18T01:25:40.949829+00:00"}