{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5WAYP3FG35GNK2C7U7UIOL6SFA","short_pith_number":"pith:5WAYP3FG","schema_version":"1.0","canonical_sha256":"ed8187eca6df4cd5685fa7e8872fd228101a351c60ac28c3e73a124caa3e0149","source":{"kind":"arxiv","id":"1908.00636","version":3},"attestation_state":"computed","paper":{"title":"Optimize TSK Fuzzy Systems for Classification Problems: Mini-Batch Gradient Descent with Uniform Regularization and Batch Normalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dongrui Wu, Jian Huang, Yuqi Cui","submitted_at":"2019-08-01T21:28:46Z","abstract_excerpt":"Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which e"},"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":"1908.00636","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-08-01T21:28:46Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b0f0911d76e50d13fb12f097e5ae5f82ab11d21a32cb78a97033dda42301e1aa","abstract_canon_sha256":"430d575cfd6dfd56222f048fd23b1033280dea769d734d96233e59f6a3b8e3fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:56:40.046742Z","signature_b64":"Q09gu64WHQQkhNvHIcShMXGbUqYAOcZe+7QuqA3RqYCuSRYtcJJ6nH0iRuAWlMJ1kj4KRuupHnw7YQrueeOQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed8187eca6df4cd5685fa7e8872fd228101a351c60ac28c3e73a124caa3e0149","last_reissued_at":"2026-07-05T01:56:40.046323Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:56:40.046323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimize TSK Fuzzy Systems for Classification Problems: Mini-Batch Gradient Descent with Uniform Regularization and Batch Normalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dongrui Wu, Jian Huang, Yuqi Cui","submitted_at":"2019-08-01T21:28:46Z","abstract_excerpt":"Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00636","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00636/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.00636","created_at":"2026-07-05T01:56:40.046381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00636v3","created_at":"2026-07-05T01:56:40.046381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00636","created_at":"2026-07-05T01:56:40.046381+00:00"},{"alias_kind":"pith_short_12","alias_value":"5WAYP3FG35GN","created_at":"2026-07-05T01:56:40.046381+00:00"},{"alias_kind":"pith_short_16","alias_value":"5WAYP3FG35GNK2C7","created_at":"2026-07-05T01:56:40.046381+00:00"},{"alias_kind":"pith_short_8","alias_value":"5WAYP3FG","created_at":"2026-07-05T01:56:40.046381+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/5WAYP3FG35GNK2C7U7UIOL6SFA","json":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA.json","graph_json":"https://pith.science/api/pith-number/5WAYP3FG35GNK2C7U7UIOL6SFA/graph.json","events_json":"https://pith.science/api/pith-number/5WAYP3FG35GNK2C7U7UIOL6SFA/events.json","paper":"https://pith.science/paper/5WAYP3FG"},"agent_actions":{"view_html":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA","download_json":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA.json","view_paper":"https://pith.science/paper/5WAYP3FG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00636&json=true","fetch_graph":"https://pith.science/api/pith-number/5WAYP3FG35GNK2C7U7UIOL6SFA/graph.json","fetch_events":"https://pith.science/api/pith-number/5WAYP3FG35GNK2C7U7UIOL6SFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA/action/storage_attestation","attest_author":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA/action/author_attestation","sign_citation":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA/action/citation_signature","submit_replication":"https://pith.science/pith/5WAYP3FG35GNK2C7U7UIOL6SFA/action/replication_record"}},"created_at":"2026-07-05T01:56:40.046381+00:00","updated_at":"2026-07-05T01:56:40.046381+00:00"}