{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:54Z","timestamp":1760242254376,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,2]],"date-time":"2017-02-02T00:00:00Z","timestamp":1485993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this paper, we address strongly convex programming for principal component analysis, which recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. In this paper, we \ufb01rstly provide suf\ufb01cient conditions under which the strongly convex models lead to the exact low-rank matrix recovery. Secondly, we also give suggestions that will guide us how to choose suitable parameters in practical algorithms. Finally, the proposed result is extended to the principal component pursuit with reduced linear measurements and we provide numerical experiments.<\/jats:p>","DOI":"10.3390\/info8010017","type":"journal-article","created":{"date-parts":[[2017,2,2]],"date-time":"2017-02-02T11:24:06Z","timestamp":1486034646000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact Solution Analysis of Strongly Convex Programming for Principal Component Pursuit"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1806-1560","authenticated-orcid":false,"given":"Qingshan","family":"You","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,2]]},"reference":[{"key":"ref_1","unstructured":"Fazel, M. (2002). Matrix Rank Minimization with Applications. [Ph.D. Thesis, Stanford University]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","article-title":"Exact matrix completion via convex optimzation","volume":"9","author":"Recht","year":"2009","journal-title":"Found. Comput. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/JPROC.2009.2035722","article-title":"Matrix completion with noise","volume":"98","author":"Plan","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The power of convex relaxation: Near-optimal matrix completion","volume":"56","author":"Tao","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ellenberg, J. Fill in the blanks: Using math to turn lo-res datasets into hi-res samples. Available online: https:\/\/www.wired.com\/2010\/02\/ff_algorithm\/all\/1.","DOI":"10.1515\/9781400839544.75"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/TPAMI.2008.79","article-title":"Robust face recognition via sparse representation","volume":"31","author":"Wright","year":"2009","journal-title":"IEEE Trans. Pattern Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s002110050258","article-title":"Image recovery via total variation minimization and related problems","volume":"76","author":"Chambolle","year":"1997","journal-title":"Numer. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1190\/1.1440378","article-title":"Robust modeling of erratic data","volume":"38","author":"Claerbout","year":"1973","journal-title":"Geophysics"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Papadimitriou, C., Raghavan, P., Tamaki, H., and Vempala, S. (1998, January 1\u20134). Latent semantic indexing: A probabilistic analysis. Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Seattle, WA, USA.","DOI":"10.1145\/275487.275505"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s10994-007-5040-8","article-title":"Convex multi-task feature learning","volume":"73","author":"Argyriou","year":"2008","journal-title":"Mach. Learn."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bouwmans, T., Sobral, A., Javed, S., Jung, S., and Zahzah, E. (2016). Decomposition into Low-rank plus Additive Matrices for Background\/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset. Comput. Vis. Pattern Recognit.","DOI":"10.1016\/j.cosrev.2016.11.001"},{"key":"ref_12","first-page":"1","article-title":"Robust principal component analysis?","volume":"58","author":"Li","year":"2009","journal-title":"J. ACM"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1090\/S0025-5718-08-02189-3","article-title":"Linearized Bregman Iterations for Compressed Sensing","volume":"78","author":"Cai","year":"2009","journal-title":"Math. Comp."},{"key":"ref_14","unstructured":"Wright, J., Ganesh, A., Rao, S., and Ma, Y. (2009). Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A singular value thresholding algorithm for matrix completion","volume":"20","author":"Cai","year":"2008","journal-title":"SIAM J. Optim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"357","DOI":"10.3934\/ipi.2012.6.357","article-title":"Strongly Convex Programming for Exact Matrix Completion and Robust Principal Component Analysis","volume":"6","author":"Zhang","year":"2012","journal-title":"Inverse Probl. Imaging"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ganesh, A., Min, K., Wright, J., and Ma, Y. (2012). Principal Component Pursuit with Reduced Linear Measurements.","DOI":"10.1109\/ISIT.2012.6283063"},{"key":"ref_18","unstructured":"Ledoux, M. (2001). The Concentration of Measure Phenomenon, American Mathematical Society."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/1\/17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:21Z","timestamp":1760207241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/1\/17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,2]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["info8010017"],"URL":"https:\/\/doi.org\/10.3390\/info8010017","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2017,2,2]]}}}