{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HGNMWEPRA7BNY2EARFLOED22FK","short_pith_number":"pith:HGNMWEPR","schema_version":"1.0","canonical_sha256":"399acb11f107c2dc68808956e20f5a2aae2ef05228e2cc4e3a108b208cb04994","source":{"kind":"arxiv","id":"1701.00757","version":1},"attestation_state":"computed","paper":{"title":"Clustering Signed Networks with the Geometric Mean of Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.NA"],"primary_cat":"stat.ML","authors_text":"Francesco Tudisco, Matthias Hein, Pedro Mercado","submitted_at":"2017-01-03T17:42:34Z","abstract_excerpt":"Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noise. Our analysis shows that these problems arise as existing approaches take some form of arithmetic mean of the Laplacians of the positive and negative part. As a solution we propose to use the geometric mean of the Laplacians of positive and negative part and show that it outpe"},"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":"1701.00757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-01-03T17:42:34Z","cross_cats_sorted":["cs.LG","math.NA"],"title_canon_sha256":"e166c182e7bb63596071a5b5884d334040eed991f9aa62385044d346e08e122a","abstract_canon_sha256":"a90bd027a527f8a5c57969139fd43568725767a5b0900dc5378d4ed2e4b27270"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:23.845746Z","signature_b64":"bCRqOdgVLD3/uDp8ubqwKFcW52QdCNNITJcBqv8VCyEWgqCGueXrli3w/03KMMa62yzDRxF9yH0uc/1GDTl7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"399acb11f107c2dc68808956e20f5a2aae2ef05228e2cc4e3a108b208cb04994","last_reissued_at":"2026-05-18T00:53:23.845186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:23.845186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clustering Signed Networks with the Geometric Mean of Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.NA"],"primary_cat":"stat.ML","authors_text":"Francesco Tudisco, Matthias Hein, Pedro Mercado","submitted_at":"2017-01-03T17:42:34Z","abstract_excerpt":"Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noise. Our analysis shows that these problems arise as existing approaches take some form of arithmetic mean of the Laplacians of the positive and negative part. As a solution we propose to use the geometric mean of the Laplacians of positive and negative part and show that it outpe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00757","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":"1701.00757","created_at":"2026-05-18T00:53:23.845274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00757v1","created_at":"2026-05-18T00:53:23.845274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00757","created_at":"2026-05-18T00:53:23.845274+00:00"},{"alias_kind":"pith_short_12","alias_value":"HGNMWEPRA7BN","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HGNMWEPRA7BNY2EA","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HGNMWEPR","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/HGNMWEPRA7BNY2EARFLOED22FK","json":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK.json","graph_json":"https://pith.science/api/pith-number/HGNMWEPRA7BNY2EARFLOED22FK/graph.json","events_json":"https://pith.science/api/pith-number/HGNMWEPRA7BNY2EARFLOED22FK/events.json","paper":"https://pith.science/paper/HGNMWEPR"},"agent_actions":{"view_html":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK","download_json":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK.json","view_paper":"https://pith.science/paper/HGNMWEPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00757&json=true","fetch_graph":"https://pith.science/api/pith-number/HGNMWEPRA7BNY2EARFLOED22FK/graph.json","fetch_events":"https://pith.science/api/pith-number/HGNMWEPRA7BNY2EARFLOED22FK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK/action/storage_attestation","attest_author":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK/action/author_attestation","sign_citation":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK/action/citation_signature","submit_replication":"https://pith.science/pith/HGNMWEPRA7BNY2EARFLOED22FK/action/replication_record"}},"created_at":"2026-05-18T00:53:23.845274+00:00","updated_at":"2026-05-18T00:53:23.845274+00:00"}