{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YVPPYQRLEOKDL635ZGGYH4GABI","short_pith_number":"pith:YVPPYQRL","schema_version":"1.0","canonical_sha256":"c55efc422b239435fb7dc98d83f0c00a3621d1b66b59a83e8020ae17177365ac","source":{"kind":"arxiv","id":"1411.1420","version":6},"attestation_state":"computed","paper":{"title":"Eigenvectors of Orthogonally Decomposable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"James Voss, Luis Rademacher, Mikhail Belkin","submitted_at":"2014-11-05T21:07:20Z","abstract_excerpt":"The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely orthogonal tensor decompositions, Independent Component Analysis (ICA), topic models, spectral clustering, and Gaussian mixture learning---we generalize the eigendecomposition from quadratic forms to a broad class of \"orthogonally decomposable\" functions. We identify a key role of convexity in our extension, and we generalize two traditional characterizations o"},"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":"1411.1420","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-11-05T21:07:20Z","cross_cats_sorted":[],"title_canon_sha256":"a65bf90a68904cc62d84fa984a623177c8ea198c2213fdf0a7ab894394e73827","abstract_canon_sha256":"14913cdd4074b1a933e5ec2e6148efb707ead99b0bef073086e200b399dd5e62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:45.101624Z","signature_b64":"kJHoYZ29iblF2R4H0KHd75M2t9+wRkmKdBQfD2XaA01ZcfWIGrOHGuGkR/5rP74T1R6zBEWhLAF+Ong2zZ1ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c55efc422b239435fb7dc98d83f0c00a3621d1b66b59a83e8020ae17177365ac","last_reissued_at":"2026-05-18T00:22:45.100989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:45.100989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvectors of Orthogonally Decomposable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"James Voss, Luis Rademacher, Mikhail Belkin","submitted_at":"2014-11-05T21:07:20Z","abstract_excerpt":"The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely orthogonal tensor decompositions, Independent Component Analysis (ICA), topic models, spectral clustering, and Gaussian mixture learning---we generalize the eigendecomposition from quadratic forms to a broad class of \"orthogonally decomposable\" functions. We identify a key role of convexity in our extension, and we generalize two traditional characterizations o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1420","kind":"arxiv","version":6},"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":"1411.1420","created_at":"2026-05-18T00:22:45.101073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1420v6","created_at":"2026-05-18T00:22:45.101073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1420","created_at":"2026-05-18T00:22:45.101073+00:00"},{"alias_kind":"pith_short_12","alias_value":"YVPPYQRLEOKD","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"YVPPYQRLEOKDL635","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"YVPPYQRL","created_at":"2026-05-18T12:28:59.999130+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/YVPPYQRLEOKDL635ZGGYH4GABI","json":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI.json","graph_json":"https://pith.science/api/pith-number/YVPPYQRLEOKDL635ZGGYH4GABI/graph.json","events_json":"https://pith.science/api/pith-number/YVPPYQRLEOKDL635ZGGYH4GABI/events.json","paper":"https://pith.science/paper/YVPPYQRL"},"agent_actions":{"view_html":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI","download_json":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI.json","view_paper":"https://pith.science/paper/YVPPYQRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1420&json=true","fetch_graph":"https://pith.science/api/pith-number/YVPPYQRLEOKDL635ZGGYH4GABI/graph.json","fetch_events":"https://pith.science/api/pith-number/YVPPYQRLEOKDL635ZGGYH4GABI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI/action/storage_attestation","attest_author":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI/action/author_attestation","sign_citation":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI/action/citation_signature","submit_replication":"https://pith.science/pith/YVPPYQRLEOKDL635ZGGYH4GABI/action/replication_record"}},"created_at":"2026-05-18T00:22:45.101073+00:00","updated_at":"2026-05-18T00:22:45.101073+00:00"}