{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2KGQRU7KRRXDJCF5LBBAIWLUFL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"250a248c06744a23706991bbdebdaa4b687302fdf518974d10e73205dc81dab4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-03-10T17:35:46Z","title_canon_sha256":"56ed78f8c5ea022c92972c1e7ed16cc42fb630f91f074c099e541d8201f0ae5f"},"schema_version":"1.0","source":{"id":"1503.03004","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03004","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03004v3","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03004","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"2KGQRU7KRRXD","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2KGQRU7KRRXDJCF5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2KGQRU7K","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:25630995deee99b3b116360f69e9dc133de3e04e749eb4b7a2aafec3e918ebd1","target":"graph","created_at":"2026-05-18T02:20:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually imposed by the physical restrictions of the system under study. Here we propose a method to perform accurate and very efficient S-FR decomposition that is more suitable for large-scale problems than existing approaches. Our method is a grateful combination of geometrical and algebraical techniques, which avoids the bottleneck caused by the Truncated SVD (TSVD).","authors_text":"German Ros, Julio Guerrero","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-03-10T17:35:46Z","title":"Fast and Robust Fixed-Rank Matrix Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03004","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b391215b846e3361e41110b6dca3e9e678bbddbf614e53b272dbc2c23cc0d7eb","target":"record","created_at":"2026-05-18T02:20:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"250a248c06744a23706991bbdebdaa4b687302fdf518974d10e73205dc81dab4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-03-10T17:35:46Z","title_canon_sha256":"56ed78f8c5ea022c92972c1e7ed16cc42fb630f91f074c099e541d8201f0ae5f"},"schema_version":"1.0","source":{"id":"1503.03004","kind":"arxiv","version":3}},"canonical_sha256":"d28d08d3ea8c6e3488bd58420459742ac2c4bca16e6f044d603dcc635f0e1983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d28d08d3ea8c6e3488bd58420459742ac2c4bca16e6f044d603dcc635f0e1983","first_computed_at":"2026-05-18T02:20:28.222202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:28.222202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrH5whHf04uq53rbtpZicaQ/ZfYZM4CVYc/4yyNX7rHkHaCkC2mWA6AcOxvRj6wH7FB79Fg2p2pwq64F5VSBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:28.222772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03004","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b391215b846e3361e41110b6dca3e9e678bbddbf614e53b272dbc2c23cc0d7eb","sha256:25630995deee99b3b116360f69e9dc133de3e04e749eb4b7a2aafec3e918ebd1"],"state_sha256":"9a2b799326f3437ab50cd115dcf9b980a5fb124ceb395cc7dfc24e14f60bc9b0"}