{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CIKL6VWIDPS33CYXW5V2HBVZUS","short_pith_number":"pith:CIKL6VWI","schema_version":"1.0","canonical_sha256":"1214bf56c81be5bd8b17b76ba386b9a48fab6288bfe02dadf486209928afa5b3","source":{"kind":"arxiv","id":"1305.0203","version":1},"attestation_state":"computed","paper":{"title":"Matrix Compression using the Nystro\\\"om Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Alon Schclar, Amir Averbuch, Arik Nemtsov","submitted_at":"2013-05-01T15:24:26Z","abstract_excerpt":"The Nystr\\\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of square matrices. We take as an input a matrix $M\\in \\mathbb{R}^{m\\times n}$, a user defined integer $s\\leq min(m,n)$ and $A_M \\in \\mathbb{R}^{s\\times s}$, a matrix sampled from the columns and rows of $M$. These are used to construct an approximate rank-$s$ SVD of $M$ in $O\\left(s^2\\left(m+n\\right)\\right)$ operations. If $M$ is square, the rank-$s$ EVD can "},"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":"1305.0203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-05-01T15:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"a40afbc9f6cd767d43486b445193df754b1fcba9ba07de2cadd17e9fe28e8923","abstract_canon_sha256":"57cd880e68cddf7132b62014edfb47b43fa9214172c2e55b094ef32e0624dae7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:41.679337Z","signature_b64":"JEztQohQBbOHYiwS/GFZEaOqHovy3cdk9+fPOWZZ+ZvLk5FbtqJ4XmrcxrIQkSKnXz9MdXr39bG+VycXvQ8vBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1214bf56c81be5bd8b17b76ba386b9a48fab6288bfe02dadf486209928afa5b3","last_reissued_at":"2026-05-18T03:26:41.678598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:41.678598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix Compression using the Nystro\\\"om Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Alon Schclar, Amir Averbuch, Arik Nemtsov","submitted_at":"2013-05-01T15:24:26Z","abstract_excerpt":"The Nystr\\\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of square matrices. We take as an input a matrix $M\\in \\mathbb{R}^{m\\times n}$, a user defined integer $s\\leq min(m,n)$ and $A_M \\in \\mathbb{R}^{s\\times s}$, a matrix sampled from the columns and rows of $M$. These are used to construct an approximate rank-$s$ SVD of $M$ in $O\\left(s^2\\left(m+n\\right)\\right)$ operations. If $M$ is square, the rank-$s$ EVD can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0203","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":"1305.0203","created_at":"2026-05-18T03:26:41.678716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0203v1","created_at":"2026-05-18T03:26:41.678716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0203","created_at":"2026-05-18T03:26:41.678716+00:00"},{"alias_kind":"pith_short_12","alias_value":"CIKL6VWIDPS3","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CIKL6VWIDPS33CYX","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CIKL6VWI","created_at":"2026-05-18T12:27:40.988391+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/CIKL6VWIDPS33CYXW5V2HBVZUS","json":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS.json","graph_json":"https://pith.science/api/pith-number/CIKL6VWIDPS33CYXW5V2HBVZUS/graph.json","events_json":"https://pith.science/api/pith-number/CIKL6VWIDPS33CYXW5V2HBVZUS/events.json","paper":"https://pith.science/paper/CIKL6VWI"},"agent_actions":{"view_html":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS","download_json":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS.json","view_paper":"https://pith.science/paper/CIKL6VWI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0203&json=true","fetch_graph":"https://pith.science/api/pith-number/CIKL6VWIDPS33CYXW5V2HBVZUS/graph.json","fetch_events":"https://pith.science/api/pith-number/CIKL6VWIDPS33CYXW5V2HBVZUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS/action/storage_attestation","attest_author":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS/action/author_attestation","sign_citation":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS/action/citation_signature","submit_replication":"https://pith.science/pith/CIKL6VWIDPS33CYXW5V2HBVZUS/action/replication_record"}},"created_at":"2026-05-18T03:26:41.678716+00:00","updated_at":"2026-05-18T03:26:41.678716+00:00"}