{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:09:56Z","timestamp":1750306196783,"version":"3.41.0"},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T00:00:00Z","timestamp":1492128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2017,8,31]]},"abstract":"<jats:p>\n            We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. In the proposed approach, we first solve an \u2113\n            <jats:sub>1<\/jats:sub>\n            -penalized version of the NP-hard sparse PCA optimization problem and then we use a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Extensive experimental evaluation indicates that the proposed approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.\n          <\/jats:p>","DOI":"10.1145\/3046948","type":"journal-article","created":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T12:18:48Z","timestamp":1492172328000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["A Randomized Rounding Algorithm for Sparse PCA"],"prefix":"10.1145","volume":"11","author":[{"given":"Kimon","family":"Fountoulakis","sequence":"first","affiliation":[{"name":"University of California Berkeley, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abhisek","family":"Kundu","sequence":"additional","affiliation":[{"name":"Xerox Research Centre India, Bangalore, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eugenia-Maria","family":"Kontopoulou","sequence":"additional","affiliation":[{"name":"Purdue University, IN, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petros","family":"Drineas","sequence":"additional","affiliation":[{"name":"Purdue University, IN, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,4,14]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2008.4595432"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/757584614"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature06258"},{"key":"e_1_2_1_4_1","first-page":"1269","article-title":"Optimal solutions for sparse principal component analysis","volume":"9","author":"Aspremont A.","year":"2008","unstructured":"A. d\u2019 Aspremont , F. Bach , and L. El Ghaoui . 2008 . Optimal solutions for sparse principal component analysis . Journal of Machine Learning Research 9 , 1269 -- 1294 . A. d\u2019Aspremont, F. Bach, and L. El Ghaoui. 2008. Optimal solutions for sparse principal component analysis. Journal of Machine Learning Research 9, 1269--1294.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_1_5_1","first-page":"1","article-title":"Approximation bounds for sparse principal component analysis","volume":"148","author":"Aspremont A.","year":"2014","unstructured":"A. d\u2019 Aspremont , F. Bach , and L. El Ghaoui . 2014 . Approximation bounds for sparse principal component analysis . Mathematical Programming, Series B 148 , 1 -- 2 , 89--110. A. d\u2019Aspremont, F. Bach, and L. El Ghaoui. 2014. Approximation bounds for sparse principal component analysis. Mathematical Programming, Series B 148, 1--2, 89--110.","journal-title":"Mathematical Programming, Series B"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/050645506"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/757584395"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1198\/1061860032148"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.5555\/1756006.1756021"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1153717"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2016.2552147"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2015.2495116"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0803205106"},{"volume-title":"Proceedings of the 23rd International Conference on Machine Learning. 641--648","author":"Moghaddam B.","key":"e_1_2_1_14_1","unstructured":"B. Moghaddam , Y. Weiss , and S. Avidan . 2012. Generalized spectral bounds for sparse LDA . In Proceedings of the 23rd International Conference on Machine Learning. 641--648 . B. Moghaddam, Y. Weiss, and S. Avidan. 2012. Generalized spectral bounds for sparse LDA. In Proceedings of the 23rd International Conference on Machine Learning. 641--648."},{"key":"e_1_2_1_15_1","volume-title":"Conference Paper, ICML (3), 747--755","author":"Papailiopoulos D. S.","year":"2013","unstructured":"D. S. Papailiopoulos , A. G. Dimakis , and S. Korokythakis . 2013. Sparse PCA through Low-rank approximations . Conference Paper, ICML (3), 747--755 . http:\/\/arxiv.org\/abs\/1303.0551 ( 2013 ). D. S. Papailiopoulos, A. G. Dimakis, and S. Korokythakis. 2013. Sparse PCA through Low-rank approximations. Conference Paper, ICML (3), 747--755. http:\/\/arxiv.org\/abs\/1303.0551 (2013)."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1136\/jmg.2010.078212"},{"key":"e_1_2_1_17_1","volume-title":"Spasm: A matlab toolbox for sparse statistical modeling. In Journal of Statistical Software (Accepted for publication).","author":"Sj\u00f6strand K.","year":"2012","unstructured":"K. Sj\u00f6strand , L. H. Clemmensen , R. Larsen , and B. Ersb\u00f8ll . 2012 . Spasm: A matlab toolbox for sparse statistical modeling. In Journal of Statistical Software (Accepted for publication). K. Sj\u00f6strand, L. H. Clemmensen, R. Larsen, and B. Ersb\u00f8ll. 2012. Spasm: A matlab toolbox for sparse statistical modeling. In Journal of Statistical Software (Accepted for publication)."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1096"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.5555\/2567709.2502610"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-28349-8_7"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1198\/106186006X113430"}],"container-title":["ACM Transactions on Knowledge Discovery from Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3046948","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3046948","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:50:24Z","timestamp":1750218624000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3046948"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,14]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,8,31]]}},"alternative-id":["10.1145\/3046948"],"URL":"https:\/\/doi.org\/10.1145\/3046948","relation":{},"ISSN":["1556-4681","1556-472X"],"issn-type":[{"type":"print","value":"1556-4681"},{"type":"electronic","value":"1556-472X"}],"subject":[],"published":{"date-parts":[[2017,4,14]]},"assertion":[{"value":"2016-06-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-04-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}