{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VX6V5H33SPPGW3AIYEASYERBYL","short_pith_number":"pith:VX6V5H33","schema_version":"1.0","canonical_sha256":"adfd5e9f7b93de6b6c08c1012c1221c2d7467ff12dc60b1a76e8ff4630fee597","source":{"kind":"arxiv","id":"1502.00727","version":7},"attestation_state":"computed","paper":{"title":"Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Daniel Korenblum","submitted_at":"2015-02-03T03:50:16Z","abstract_excerpt":"Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximatio"},"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":"1502.00727","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-02-03T03:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"6241449bcb77af355afe348a39036abc1615d4f52e213f3fb55ce7b49a0f5601","abstract_canon_sha256":"65e424afde79ba5af78f4e029bba8c6c6aac33db19c3245517abdc8b93963c27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:24.476819Z","signature_b64":"oTDFwLPzxKJYaC9qHLYW69pe258+mzfA4eL9mHMUwLRKVZ6bN8xf7YEaxY9eQQY4fFwA89ypJVhwj79T3e44Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adfd5e9f7b93de6b6c08c1012c1221c2d7467ff12dc60b1a76e8ff4630fee597","last_reissued_at":"2026-05-18T00:04:24.476298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:24.476298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Daniel Korenblum","submitted_at":"2015-02-03T03:50:16Z","abstract_excerpt":"Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00727","kind":"arxiv","version":7},"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":"1502.00727","created_at":"2026-05-18T00:04:24.476387+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00727v7","created_at":"2026-05-18T00:04:24.476387+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00727","created_at":"2026-05-18T00:04:24.476387+00:00"},{"alias_kind":"pith_short_12","alias_value":"VX6V5H33SPPG","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VX6V5H33SPPGW3AI","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VX6V5H33","created_at":"2026-05-18T12:29:47.479230+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/VX6V5H33SPPGW3AIYEASYERBYL","json":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL.json","graph_json":"https://pith.science/api/pith-number/VX6V5H33SPPGW3AIYEASYERBYL/graph.json","events_json":"https://pith.science/api/pith-number/VX6V5H33SPPGW3AIYEASYERBYL/events.json","paper":"https://pith.science/paper/VX6V5H33"},"agent_actions":{"view_html":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL","download_json":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL.json","view_paper":"https://pith.science/paper/VX6V5H33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00727&json=true","fetch_graph":"https://pith.science/api/pith-number/VX6V5H33SPPGW3AIYEASYERBYL/graph.json","fetch_events":"https://pith.science/api/pith-number/VX6V5H33SPPGW3AIYEASYERBYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL/action/storage_attestation","attest_author":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL/action/author_attestation","sign_citation":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL/action/citation_signature","submit_replication":"https://pith.science/pith/VX6V5H33SPPGW3AIYEASYERBYL/action/replication_record"}},"created_at":"2026-05-18T00:04:24.476387+00:00","updated_at":"2026-05-18T00:04:24.476387+00:00"}