{"paper":{"title":"Fast computation of the principal components of genotype matrices in Julia","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","q-bio.GN","stat.AP"],"primary_cat":"math.NA","authors_text":"Alan Edelman, Andreas Noack, Jiahao Chen","submitted_at":"2018-08-09T23:47:21Z","abstract_excerpt":"Finding the largest few principal components of a matrix of genetic data is a common task in genome-wide association studies (GWASs), both for dimensionality reduction and for identifying unwanted factors of variation. We describe a simple random matrix model for matrices that arise in GWASs, showing that the singular values have a bulk behavior that obeys a Marchenko-Pastur distributed with a handful of large outliers. We also implement Golub-Kahan-Lanczos (GKL) bidiagonalization in the Julia programming language, providing thick restarting and a choice between full and partial reorthogonaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03374","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"}