{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/single-pass-pca-of-matrix-products","title":"Single Pass PCA of Matrix Products","arxiv_id":"1610.06656","date":"2016-10-21","proceeding":"NeurIPS 2016 12","authors":["Shanshan Wu","Srinadh Bhojanapalli","Sujay Sanghavi","Alexandros G. Dimakis"],"abstract":"In this paper we present a new algorithm for computing a low rank\napproximation of the product $A^TB$ by taking only a single pass of the two\nmatrices $A$ and $B$. The straightforward way to do this is to (a) first sketch\n$A$ and $B$ individually, and then (b) find the top components using PCA on the\nsketch. Our algorithm in contrast retains additional summary information about\n$A,B$ (e.g. row and column norms etc.) and uses this additional information to\nobtain an improved approximation from the sketches. Our main analytical result\nestablishes a comparable spectral norm guarantee to existing two-pass methods;\nin addition we also provide results from an Apache Spark implementation that\nshows better computational and statistical performance on real-world and\nsynthetic evaluation datasets.","url_abs":"http://arxiv.org/abs/1610.06656v2","url_pdf":"http://arxiv.org/pdf/1610.06656v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"single-pass-pca-of-matrix-products","repo_url":"https://github.com/wushanshan/MatrixProductPCA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1610.06656","atlas_url":"https://app.syntology.ai/?focus=1610.06656","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}