{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FZJ7PFPINOX56MSORAXL2WRWAG","short_pith_number":"pith:FZJ7PFPI","schema_version":"1.0","canonical_sha256":"2e53f795e86bafdf324e882ebd5a3601aaf5689fc69d2382bff547fc2206f45f","source":{"kind":"arxiv","id":"1301.3192","version":1},"attestation_state":"computed","paper":{"title":"Matrix Approximation under Local Low-Rank Assumption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Guy Lebanon, Joonseok Lee, Seungyeon Kim, Yoram Singer","submitted_at":"2013-01-15T00:54:38Z","abstract_excerpt":"Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is only locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low-rank matrices. We analyze the accuracy of the proposed local low-rank modeling. Our experiments show improvements in prediction accuracy"},"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":"1301.3192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-01-15T00:54:38Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"30947b31114a97647f91aa37710b1d584d2e682ee9bd61ac4b42a6c667abc874","abstract_canon_sha256":"45937efd6b2b9a6e35208bcbfe3cda5149a9f2a2b9358ec4e49b73d385413100"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:26.264781Z","signature_b64":"h2l6kklWiwf5TgYk15Ydh/v6OpOEFhePymEXlidlmZrIjps+6QXKVnB+KtwacopsjxYxTb+yEcvK0VOBCeqRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e53f795e86bafdf324e882ebd5a3601aaf5689fc69d2382bff547fc2206f45f","last_reissued_at":"2026-05-18T03:36:26.264037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:26.264037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix Approximation under Local Low-Rank Assumption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Guy Lebanon, Joonseok Lee, Seungyeon Kim, Yoram Singer","submitted_at":"2013-01-15T00:54:38Z","abstract_excerpt":"Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is only locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low-rank matrices. We analyze the accuracy of the proposed local low-rank modeling. Our experiments show improvements in prediction accuracy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3192","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":"1301.3192","created_at":"2026-05-18T03:36:26.264158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3192v1","created_at":"2026-05-18T03:36:26.264158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3192","created_at":"2026-05-18T03:36:26.264158+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZJ7PFPINOX5","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZJ7PFPINOX56MSO","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZJ7PFPI","created_at":"2026-05-18T12:27:45.050594+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/FZJ7PFPINOX56MSORAXL2WRWAG","json":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG.json","graph_json":"https://pith.science/api/pith-number/FZJ7PFPINOX56MSORAXL2WRWAG/graph.json","events_json":"https://pith.science/api/pith-number/FZJ7PFPINOX56MSORAXL2WRWAG/events.json","paper":"https://pith.science/paper/FZJ7PFPI"},"agent_actions":{"view_html":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG","download_json":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG.json","view_paper":"https://pith.science/paper/FZJ7PFPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3192&json=true","fetch_graph":"https://pith.science/api/pith-number/FZJ7PFPINOX56MSORAXL2WRWAG/graph.json","fetch_events":"https://pith.science/api/pith-number/FZJ7PFPINOX56MSORAXL2WRWAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG/action/storage_attestation","attest_author":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG/action/author_attestation","sign_citation":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG/action/citation_signature","submit_replication":"https://pith.science/pith/FZJ7PFPINOX56MSORAXL2WRWAG/action/replication_record"}},"created_at":"2026-05-18T03:36:26.264158+00:00","updated_at":"2026-05-18T03:36:26.264158+00:00"}