{"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"}