{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZJJYP233ZK2TYRAPKICIYNZMCH","short_pith_number":"pith:ZJJYP233","schema_version":"1.0","canonical_sha256":"ca5387eb7bcab53c440f52048c372c11e92509fcf6d85ee2fb19786ac5185014","source":{"kind":"arxiv","id":"1605.05349","version":1},"attestation_state":"computed","paper":{"title":"Orthogonal symmetric non-negative matrix factorization under the stochastic block model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Subhadeep Paul, Yuguo Chen","submitted_at":"2016-05-17T20:22:12Z","abstract_excerpt":"We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimization problem. We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering. Using such factorization for clustering in networks is motivated b"},"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":"1605.05349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-05-17T20:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"d3d237d59c9b92361b7637f63c6fd2a4628bcd56878afab72bca9245dd3d7281","abstract_canon_sha256":"42fd8bf6fb131eef7e2d159ec44e8422afa164369e801b88d1a40d69cf3017bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:35.213158Z","signature_b64":"eNvIM9n6eShxPLvw5wgQZ0CxivstoEeLvV+cGa5FO/qRUTvaWmAmU/cmafVEO6Xaz9z/dLcB5+r+/uAsEczRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca5387eb7bcab53c440f52048c372c11e92509fcf6d85ee2fb19786ac5185014","last_reissued_at":"2026-05-18T01:14:35.212430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:35.212430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal symmetric non-negative matrix factorization under the stochastic block model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Subhadeep Paul, Yuguo Chen","submitted_at":"2016-05-17T20:22:12Z","abstract_excerpt":"We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimization problem. We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering. Using such factorization for clustering in networks is motivated b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05349","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":"1605.05349","created_at":"2026-05-18T01:14:35.212545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05349v1","created_at":"2026-05-18T01:14:35.212545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05349","created_at":"2026-05-18T01:14:35.212545+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZJJYP233ZK2T","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZJJYP233ZK2TYRAP","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZJJYP233","created_at":"2026-05-18T12:30:53.716459+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2601.06262","citing_title":"Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH","json":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH.json","graph_json":"https://pith.science/api/pith-number/ZJJYP233ZK2TYRAPKICIYNZMCH/graph.json","events_json":"https://pith.science/api/pith-number/ZJJYP233ZK2TYRAPKICIYNZMCH/events.json","paper":"https://pith.science/paper/ZJJYP233"},"agent_actions":{"view_html":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH","download_json":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH.json","view_paper":"https://pith.science/paper/ZJJYP233","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05349&json=true","fetch_graph":"https://pith.science/api/pith-number/ZJJYP233ZK2TYRAPKICIYNZMCH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZJJYP233ZK2TYRAPKICIYNZMCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH/action/storage_attestation","attest_author":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH/action/author_attestation","sign_citation":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH/action/citation_signature","submit_replication":"https://pith.science/pith/ZJJYP233ZK2TYRAPKICIYNZMCH/action/replication_record"}},"created_at":"2026-05-18T01:14:35.212545+00:00","updated_at":"2026-05-18T01:14:35.212545+00:00"}