{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7JPHNJYOFLIAY235MF2NPVOC5D","short_pith_number":"pith:7JPHNJYO","canonical_record":{"source":{"id":"1607.02024","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2016-07-07T14:06:06Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"38a56bbe4054cbcfefa5fdedd1acec28b8239d7f6cf63eb46286c84092a628f5","abstract_canon_sha256":"9272dac582762a996c17c518d7097d7efcae9eb6450b56a86cfcfa3648988896"},"schema_version":"1.0"},"canonical_sha256":"fa5e76a70e2ad00c6b7d6174d7d5c2e8d2f39fc5d976036fdcbbc56e09eaf407","source":{"kind":"arxiv","id":"1607.02024","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02024","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02024v2","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02024","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"7JPHNJYOFLIA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7JPHNJYOFLIAY235","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7JPHNJYO","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7JPHNJYOFLIAY235MF2NPVOC5D","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02024","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2016-07-07T14:06:06Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"38a56bbe4054cbcfefa5fdedd1acec28b8239d7f6cf63eb46286c84092a628f5","abstract_canon_sha256":"9272dac582762a996c17c518d7097d7efcae9eb6450b56a86cfcfa3648988896"},"schema_version":"1.0"},"canonical_sha256":"fa5e76a70e2ad00c6b7d6174d7d5c2e8d2f39fc5d976036fdcbbc56e09eaf407","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:11.624600Z","signature_b64":"5DTQatQOpxnq+a14RguJZ+k65gGdi/j9y3xjhNwM+hKCAXOeV5NsqiQgt/4mkyTh5I+9F+YpBIS0nUukZVScCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa5e76a70e2ad00c6b7d6174d7d5c2e8d2f39fc5d976036fdcbbc56e09eaf407","last_reissued_at":"2026-05-18T01:09:11.624130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:11.624130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02024","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":"2026-05-18T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NGXmGQf8NAFBdgNIzIfXScSnbMhBdFyGb+9s87gSwrVtpMQ3bnx1lLUnmIhxwA6we71VLyGOtx5n5SnV5pKRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:58:17.885784Z"},"content_sha256":"1e14fe017310b95869a2ab02f07d97fe7f4f4e643074029c3ab906db7fe425f4","schema_version":"1.0","event_id":"sha256:1e14fe017310b95869a2ab02f07d97fe7f4f4e643074029c3ab906db7fe425f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7JPHNJYOFLIAY235MF2NPVOC5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mini-Batch Spectral Clustering","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Maurizio Filippone, Yufei Han","submitted_at":"2016-07-07T14:06:06Z","abstract_excerpt":"The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive stochastic gradient optimization. Crucially, the proposed approach recovers the exact spectrum of Laplacian matrices in the limit of the iterations, and the cost of each iteration is linear in the number of samples. Extensive experimental validation on data sets with up to half "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02024","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":"2026-05-18T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BViKwRetSGY69YyKIIqw4XHhH5KDzoO7WpOsLWC1A3QzgWZ3qGRAwpEQ2VPG4a9Qsc7TNgauZ/RCtIH/mTKzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:58:17.886110Z"},"content_sha256":"b6cbb2acd89f3b6faf9efaae6f4761212ff6595a40c15bdc1726b60e2c7ddebe","schema_version":"1.0","event_id":"sha256:b6cbb2acd89f3b6faf9efaae6f4761212ff6595a40c15bdc1726b60e2c7ddebe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JPHNJYOFLIAY235MF2NPVOC5D/bundle.json","state_url":"https://pith.science/pith/7JPHNJYOFLIAY235MF2NPVOC5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JPHNJYOFLIAY235MF2NPVOC5D/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":"2026-06-27T19:58:17Z","links":{"resolver":"https://pith.science/pith/7JPHNJYOFLIAY235MF2NPVOC5D","bundle":"https://pith.science/pith/7JPHNJYOFLIAY235MF2NPVOC5D/bundle.json","state":"https://pith.science/pith/7JPHNJYOFLIAY235MF2NPVOC5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JPHNJYOFLIAY235MF2NPVOC5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7JPHNJYOFLIAY235MF2NPVOC5D","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":"9272dac582762a996c17c518d7097d7efcae9eb6450b56a86cfcfa3648988896","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2016-07-07T14:06:06Z","title_canon_sha256":"38a56bbe4054cbcfefa5fdedd1acec28b8239d7f6cf63eb46286c84092a628f5"},"schema_version":"1.0","source":{"id":"1607.02024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02024","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02024v2","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02024","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"7JPHNJYOFLIA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7JPHNJYOFLIAY235","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7JPHNJYO","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:b6cbb2acd89f3b6faf9efaae6f4761212ff6595a40c15bdc1726b60e2c7ddebe","target":"graph","created_at":"2026-05-18T01:09:11Z","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":"The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive stochastic gradient optimization. Crucially, the proposed approach recovers the exact spectrum of Laplacian matrices in the limit of the iterations, and the cost of each iteration is linear in the number of samples. Extensive experimental validation on data sets with up to half ","authors_text":"Maurizio Filippone, Yufei Han","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2016-07-07T14:06:06Z","title":"Mini-Batch Spectral Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02024","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":"sha256:1e14fe017310b95869a2ab02f07d97fe7f4f4e643074029c3ab906db7fe425f4","target":"record","created_at":"2026-05-18T01:09:11Z","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":"9272dac582762a996c17c518d7097d7efcae9eb6450b56a86cfcfa3648988896","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2016-07-07T14:06:06Z","title_canon_sha256":"38a56bbe4054cbcfefa5fdedd1acec28b8239d7f6cf63eb46286c84092a628f5"},"schema_version":"1.0","source":{"id":"1607.02024","kind":"arxiv","version":2}},"canonical_sha256":"fa5e76a70e2ad00c6b7d6174d7d5c2e8d2f39fc5d976036fdcbbc56e09eaf407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa5e76a70e2ad00c6b7d6174d7d5c2e8d2f39fc5d976036fdcbbc56e09eaf407","first_computed_at":"2026-05-18T01:09:11.624130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:11.624130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5DTQatQOpxnq+a14RguJZ+k65gGdi/j9y3xjhNwM+hKCAXOeV5NsqiQgt/4mkyTh5I+9F+YpBIS0nUukZVScCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:11.624600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e14fe017310b95869a2ab02f07d97fe7f4f4e643074029c3ab906db7fe425f4","sha256:b6cbb2acd89f3b6faf9efaae6f4761212ff6595a40c15bdc1726b60e2c7ddebe"],"state_sha256":"bbe0d5fe0216a950f9dabdfd4cde9a197227e6a6cc8e6688ba9ddba23884d407"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FWRsEOl8vmlNaMVP8ymJyIGA9PuTSzmrSsG/gK4buIN84VIB+io2QZPVgkNLRhPUgAZhvdow+issNMyk+0sWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T19:58:17.887911Z","bundle_sha256":"47e09908f54d8b61e8e527e2260d89066ba14434c4ea513ea45d8ebcf8e8baaa"}}