{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HBDIH7OEPL5D76YPMKXVZGIQL5","short_pith_number":"pith:HBDIH7OE","schema_version":"1.0","canonical_sha256":"384683fdc47afa3ffb0f62af5c99105f56a80c42104ac180089f1468b5008993","source":{"kind":"arxiv","id":"1801.08196","version":1},"attestation_state":"computed","paper":{"title":"Incremental Eigenpair Computation for Graph Laplacian Matrices: Theory and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Baichuan Zhang, Mohammad Al Hasan, Pin-Yu Chen","submitted_at":"2017-12-13T19:04:35Z","abstract_excerpt":"The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, $K$) is generally unknown a-priori. Consequently, the majority of the existing methods either choose $K$ heuristically or they repeat the clustering method with different choices of $K$ and accept the best clustering result. The first option, more often, yields suboptimal result, while the second option is computationally expensive. In this work"},"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":"1801.08196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-13T19:04:35Z","cross_cats_sorted":["cs.SI","stat.ML"],"title_canon_sha256":"999c4ede19551895f241b4b697947f3052e44e09458dc671466217c916157ca3","abstract_canon_sha256":"ba4bc6d3a1c9a6f7c3ea00f3cbc849324c2fb87cac20fd6c66d678fc77fc343d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:06.864406Z","signature_b64":"dBdqyPLG6x83Gcw+MiFXkfGoPO5dV/AG0JKjWySdD4fmynWAadFTqK83HTRPHMo1QdjdmgQjb6IJvFwvjMjLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"384683fdc47afa3ffb0f62af5c99105f56a80c42104ac180089f1468b5008993","last_reissued_at":"2026-05-18T00:25:06.863979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:06.863979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incremental Eigenpair Computation for Graph Laplacian Matrices: Theory and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Baichuan Zhang, Mohammad Al Hasan, Pin-Yu Chen","submitted_at":"2017-12-13T19:04:35Z","abstract_excerpt":"The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, $K$) is generally unknown a-priori. Consequently, the majority of the existing methods either choose $K$ heuristically or they repeat the clustering method with different choices of $K$ and accept the best clustering result. The first option, more often, yields suboptimal result, while the second option is computationally expensive. In this work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08196","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":"1801.08196","created_at":"2026-05-18T00:25:06.864049+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08196v1","created_at":"2026-05-18T00:25:06.864049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08196","created_at":"2026-05-18T00:25:06.864049+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBDIH7OEPL5D","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBDIH7OEPL5D76YP","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBDIH7OE","created_at":"2026-05-18T12:31:18.294218+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/HBDIH7OEPL5D76YPMKXVZGIQL5","json":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5.json","graph_json":"https://pith.science/api/pith-number/HBDIH7OEPL5D76YPMKXVZGIQL5/graph.json","events_json":"https://pith.science/api/pith-number/HBDIH7OEPL5D76YPMKXVZGIQL5/events.json","paper":"https://pith.science/paper/HBDIH7OE"},"agent_actions":{"view_html":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5","download_json":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5.json","view_paper":"https://pith.science/paper/HBDIH7OE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08196&json=true","fetch_graph":"https://pith.science/api/pith-number/HBDIH7OEPL5D76YPMKXVZGIQL5/graph.json","fetch_events":"https://pith.science/api/pith-number/HBDIH7OEPL5D76YPMKXVZGIQL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5/action/storage_attestation","attest_author":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5/action/author_attestation","sign_citation":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5/action/citation_signature","submit_replication":"https://pith.science/pith/HBDIH7OEPL5D76YPMKXVZGIQL5/action/replication_record"}},"created_at":"2026-05-18T00:25:06.864049+00:00","updated_at":"2026-05-18T00:25:06.864049+00:00"}