{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2IJZTTNMUVWKW6FOGZINCE7ZXH","short_pith_number":"pith:2IJZTTNM","schema_version":"1.0","canonical_sha256":"d21399cdaca56cab78ae3650d113f9b9eb012edc6b857dc8fefbbc49e05b4a1c","source":{"kind":"arxiv","id":"1509.05647","version":4},"attestation_state":"computed","paper":{"title":"Fast and Simple PCA via Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Dan Garber, Elad Hazan","submitted_at":"2015-09-18T15:03:03Z","abstract_excerpt":"The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \\textit{small} number of well-conditioned {\\it convex} optimization problems. This gives rise to a new efficient method for PCA based on recent advances in stochastic methods for convex optimization.\n  In particular we show that given a $d\\times d$ matrix $\\X = \\frac{1}{n}\\sum_{i=1}^n\\x_i\\x_i^{\\top}$ with top eigenvector $\\u$ and top eigenvalue $\\lambda_1$ it is possible to: \\begin{itemize} \\item compute "},"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":"1509.05647","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-18T15:03:03Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"d6f517eeca7477d5f3a0e963a14378968205be710ee11fe37a84c3698abcbd53","abstract_canon_sha256":"efb2c314b160fca71e2c5553b77f796da5dcebf81644f21baa640b29244ef21c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:02.522483Z","signature_b64":"BSEEHdu/O4ht8GUpw12bmtbSGhBH92nVD61oxbi4OWJ037A1cue1DWyGU5d6XVo/Vi4dmcoT8Xl3yuxWuoDNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d21399cdaca56cab78ae3650d113f9b9eb012edc6b857dc8fefbbc49e05b4a1c","last_reissued_at":"2026-05-18T01:26:02.521906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:02.521906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast and Simple PCA via Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Dan Garber, Elad Hazan","submitted_at":"2015-09-18T15:03:03Z","abstract_excerpt":"The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \\textit{small} number of well-conditioned {\\it convex} optimization problems. This gives rise to a new efficient method for PCA based on recent advances in stochastic methods for convex optimization.\n  In particular we show that given a $d\\times d$ matrix $\\X = \\frac{1}{n}\\sum_{i=1}^n\\x_i\\x_i^{\\top}$ with top eigenvector $\\u$ and top eigenvalue $\\lambda_1$ it is possible to: \\begin{itemize} \\item compute "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05647","kind":"arxiv","version":4},"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":"1509.05647","created_at":"2026-05-18T01:26:02.521997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05647v4","created_at":"2026-05-18T01:26:02.521997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05647","created_at":"2026-05-18T01:26:02.521997+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IJZTTNMUVWK","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IJZTTNMUVWKW6FO","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IJZTTNM","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2003.00295","citing_title":"Adaptive Federated Optimization","ref_index":157,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH","json":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH.json","graph_json":"https://pith.science/api/pith-number/2IJZTTNMUVWKW6FOGZINCE7ZXH/graph.json","events_json":"https://pith.science/api/pith-number/2IJZTTNMUVWKW6FOGZINCE7ZXH/events.json","paper":"https://pith.science/paper/2IJZTTNM"},"agent_actions":{"view_html":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH","download_json":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH.json","view_paper":"https://pith.science/paper/2IJZTTNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05647&json=true","fetch_graph":"https://pith.science/api/pith-number/2IJZTTNMUVWKW6FOGZINCE7ZXH/graph.json","fetch_events":"https://pith.science/api/pith-number/2IJZTTNMUVWKW6FOGZINCE7ZXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH/action/storage_attestation","attest_author":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH/action/author_attestation","sign_citation":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH/action/citation_signature","submit_replication":"https://pith.science/pith/2IJZTTNMUVWKW6FOGZINCE7ZXH/action/replication_record"}},"created_at":"2026-05-18T01:26:02.521997+00:00","updated_at":"2026-05-18T01:26:02.521997+00:00"}