{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T17:25:37Z","timestamp":1743009937853,"version":"3.40.3"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319181608"},{"type":"electronic","value":"9783319181615"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-18161-5_12","type":"book-chapter","created":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T08:51:26Z","timestamp":1430383886000},"page":"131-142","source":"Crossref","is-referenced-by-count":0,"title":["A DC Programming Approach for Sparse Estimation of a Covariance Matrix"],"prefix":"10.1007","author":[{"given":"Duy Nhat","family":"Phan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hoai An","family":"Le Thi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao Pham","family":"Dinh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"6","key":"12_CR1","doi-asserted-by":"publisher","first-page":"989","DOI":"10.3150\/bj\/1106314847","volume":"10","author":"P.J. Bickel","year":"2004","unstructured":"Bickel, P.J., Levina, E.: Some theory for Fisher\u2019s linear discriminant function, naive Bayes, and some alternatives when there are many more variables than observations. Bernoulli\u00a010(6), 989\u20131010 (2004)","journal-title":"Bernoulli"},{"key":"12_CR2","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1214\/009053607000000758","volume":"36","author":"P.J. Bickel","year":"2008","unstructured":"Bickel, P.J., Levina, E.: Regularized estimation of large covariance matrices. The Annals of Statistichs\u00a036, 199\u2013227 (2008)","journal-title":"The Annals of Statistichs"},{"issue":"4","key":"12_CR3","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1093\/biomet\/asr054","volume":"98","author":"J. Bien","year":"2011","unstructured":"Bien, J., Tibshirani, R.: Sparse estimation of a covariance matrix. Biometrika\u00a098(4), 807\u2013820 (2011)","journal-title":"Biometrika"},{"issue":"1","key":"12_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S. Boyd","year":"2011","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundat. Trends Mach. Learn.\u00a03(1), 1\u2013122 (2011)","journal-title":"Foundat. Trends Mach. Learn."},{"key":"12_CR5","doi-asserted-by":"publisher","first-page":"2118","DOI":"10.1214\/09-AOS752","volume":"38","author":"T. Cai","year":"2010","unstructured":"Cai, T., Zhang, C., Zou, H.: Optimal rates of convergence for covariance matrix estimation. The Annals of Statistic\u00a038, 2118\u20132144 (2010)","journal-title":"The Annals of Statistic"},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1093\/biomet\/asm007","volume":"94","author":"S. Chaudhuri","year":"2007","unstructured":"Chaudhuri, S., Drton, M., Richardson, T.S.: Estimation of a covariance matrix with zeros. Biometrika\u00a094, 199\u2013216 (2007)","journal-title":"Biometrika"},{"key":"12_CR7","unstructured":"Fawzi, A., Davies, M., Frossard, P.: Dictionary learning for fast classification based on soft-thresholding. International Journal of Computer Vision (2014), \n                      http:\/\/arxiv.org\/abs\/1402.1973"},{"key":"12_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning","author":"T. Hastie","year":"2009","unstructured":"Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning, 2nd edn. Springer, New York (2009)","edition":"2"},{"key":"12_CR9","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1093\/biomet\/93.1.85","volume":"93","author":"J.Z. Huang","year":"2006","unstructured":"Huang, J.Z., Liu, N., Pourahmadi, M., Liu, L.: Covariance matrix selection and estimation via penalised normal likelihood. Biometrika\u00a093, 85\u201398 (2006)","journal-title":"Biometrika"},{"key":"12_CR10","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1214\/10-AOS841","volume":"39","author":"K. Khare","year":"2011","unstructured":"Khare, K., Rajaratnam, B.: Wishart distributions for decomposable covariance graph models. Ann. Statist.\u00a039, 514\u2013555 (2011)","journal-title":"Ann. Statist."},{"key":"12_CR11","doi-asserted-by":"publisher","first-page":"4254","DOI":"10.1214\/09-AOS720","volume":"37","author":"C. Lam","year":"2009","unstructured":"Lam, C., Fan, J.: Sparsistency and rates of convergence in large covariance matrix estimation. The Annals of Statistics\u00a037, 4254\u20134278 (2009)","journal-title":"The Annals of Statistics"},{"issue":"3","key":"12_CR12","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/s10898-011-9765-3","volume":"52","author":"H.A. Le Thi","year":"2012","unstructured":"Le Thi, H.A., Huynh Van, N., Pham Dinh, T.: Exact penalty and error bounds in DC programming. Journal of Global Optimization\u00a052(3), 509\u2013535 (2012)","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"12_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s11634-008-0030-7","volume":"2","author":"H.A. Le Thi","year":"2008","unstructured":"Le Thi, H.A., Le Hoai, M., Nguyen, V.V., Pham Dinh, T.: A DC Programming approach for feature selection in support vector machines learning. Journal of Advances in Data Analysis and Classification\u00a02(3), 259\u2013278 (2008)","journal-title":"Journal of Advances in Data Analysis and Classification"},{"key":"12_CR14","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1016\/j.ejor.2005.07.028","volume":"183","author":"H.A. Le Thi","year":"2007","unstructured":"Le Thi, H.A., Le Hoai, M., Pham Dinh, T.: Optimization based DC programming and DCA for hierarchical clustering. European Journal of Operational Research\u00a0183, 1067\u20131085 (2007)","journal-title":"European Journal of Operational Research"},{"key":"12_CR15","doi-asserted-by":"crossref","unstructured":"Le Thi, H.A., Le Hoai, M., Pham Dinh, T.: Feature selection in machine learning: An exact penalty approachusing a difference of convex function algorithm. Machine Learning (2014), (published online July 04, 2014), doi:10.1007\/s10994-014-5455-y","DOI":"10.1007\/s10994-014-5455-y"},{"key":"12_CR16","doi-asserted-by":"publisher","first-page":"1336","DOI":"10.1007\/s10618-014-0369-7","volume":"28","author":"H.A. Le Thi","year":"2014","unstructured":"Le Thi, H.A., Nguyen, M.C.: Self-organizing maps by difference of convex functions optimization. Data Mining and Knowledge Discovery\u00a028, 1336\u20131365 (2014)","journal-title":"Data Mining and Knowledge Discovery"},{"key":"12_CR17","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1008288411710","volume":"11","author":"H.A. Le Thi","year":"1997","unstructured":"Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by D.C. algorithms. Journal of Global Optimization\u00a011, 253\u2013285 (1997)","journal-title":"Journal of Global Optimization"},{"key":"12_CR18","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"H.A. Le Thi","year":"2005","unstructured":"Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research\u00a0133, 23\u201346 (2005)","journal-title":"Annals of Operations Research"},{"key":"12_CR19","doi-asserted-by":"crossref","unstructured":"Le Thi, H.A., Pham Dinh, T., Le Hoai, M., Vo Xuan, T.: DC approximation approaches for sparse optimization. To appear in European Journal of Operational Research (2014)","DOI":"10.1016\/j.ejor.2014.11.031"},{"key":"12_CR20","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.neunet.2014.06.011","volume":"59","author":"H.A. Le Thi","year":"2014","unstructured":"Le Thi, H.A., Vo Xuan, T., Pham Dinh, T.: Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions Algorithms. Neural Networks\u00a059, 36\u201350 (2014)","journal-title":"Neural Networks"},{"issue":"1","key":"12_CR21","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1214\/07-AOAS139","volume":"2","author":"E. Levina","year":"2008","unstructured":"Levina, E., Rothman, A., Zhu, J.: Sparse estimation of large covariance matrices via a nested lasso penalty. Ann. Appl. Stat.\u00a02(1), 245\u2013263 (2008)","journal-title":"Ann. Appl. Stat."},{"issue":"2","key":"12_CR22","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1080\/10618600.2013.782818","volume":"23","author":"H. Liu","year":"2014","unstructured":"Liu, H., Wang, L., Zhao, T.: Sparse covariance matrix estimation with eigenvalue contraints. Journal of Computational and Graphical Statistics\u00a023(2), 439\u2013459 (2014)","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"12_CR23","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1198\/016214505000000781","volume":"101","author":"Y. Liu","year":"2006","unstructured":"Liu, Y., Shen, X.: Multicategory \u03c8-Learning. Journal of the American Statistical Association\u00a0101, 500\u2013509 (2006)","journal-title":"Journal of the American Statistical Association"},{"key":"12_CR24","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1198\/106186005X37238","volume":"14","author":"Y. Liu","year":"2005","unstructured":"Liu, Y., Shen, X., Doss, H.: Multicategory \u03c8-Learning and Support Vector Machine: Computational Tools. Journal of Computational and Graphical Statistics\u00a014, 219\u2013236 (2005)","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"12_CR25","unstructured":"Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic (1979)"},{"issue":"1","key":"12_CR26","first-page":"289","volume":"22","author":"T. Pham Dinh","year":"1997","unstructured":"Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to D.C. programming: Theory, algorithms and applications. Acta Mathematica Vietnamica\u00a022(1), 289\u2013355 (1997)","journal-title":"Acta Mathematica Vietnamica"},{"issue":"1","key":"12_CR27","first-page":"476","volume":"8","author":"T. Pham Dinh","year":"1998","unstructured":"Pham Dinh, T., Le Thi, H.A.: DC optimization algorithm for solving the trust-region subproblem. SIAM Journal of Optimization\u00a08(1), 476\u2013505 (1998)","journal-title":"SIAM Journal of Optimization"},{"key":"12_CR28","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1198\/jasa.2009.0101","volume":"104","author":"A.J. Rothman","year":"2009","unstructured":"Rothman, A.J., Levina, E., Zhu, J.: Generalized thresholding of large covariance matrices. J. Am. Statist. Assoc.\u00a0104, 177\u2013186 (2009)","journal-title":"J. Am. Statist. Assoc."},{"key":"12_CR29","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1093\/biomet\/asq022","volume":"97","author":"A.J. Rothman","year":"2010","unstructured":"Rothman, A.J., Levina, E., Zhu, J.: A new approach to Cholesky-based covariance regularization in high dimensions. Biometrika\u00a097, 539\u2013550 (2010)","journal-title":"Biometrika"},{"key":"12_CR30","series-title":"CCIS","first-page":"348","volume-title":"MCO 2008","author":"M. Thiao","year":"2008","unstructured":"Thiao, M., Pham Dinh, T., Le Thi, H.A.: DC Programming. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) MCO 2008. CCIS, vol.\u00a014, pp. 348\u2013357. Springer, Heidelberg (2008)"}],"container-title":["Advances in Intelligent Systems and Computing","Modelling, Computation and Optimization in Information Systems and Management Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-18161-5_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T05:19:22Z","timestamp":1676956762000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-18161-5_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319181608","9783319181615"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-18161-5_12","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2015]]}}}