{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:21:34Z","timestamp":1740108094434,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T00:00:00Z","timestamp":1562112000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T00:00:00Z","timestamp":1562112000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["2015XKMS084"],"award-info":[{"award-number":["2015XKMS084"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s10044-019-00834-y","type":"journal-article","created":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T11:03:34Z","timestamp":1562151814000},"page":"735-749","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Locality preserving difference component analysis based on the Lq norm"],"prefix":"10.1007","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2626-2554","authenticated-orcid":false,"given":"Zhizheng","family":"Liang","sequence":"first","affiliation":[]},{"given":"Xuewen","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Jin","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Yong","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,3]]},"reference":[{"key":"834_CR1","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1109\/34.598228","volume":"19","author":"PN Belhumeur","year":"1997","unstructured":"Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. Fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19:711\u2013720","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"834_CR2","doi-asserted-by":"crossref","unstructured":"Baccini A, Besse P, Falguerolles AD (1996) A L1-norm PCA and A heuristic approach. Ordinal Symbol Data Anal 1:359-368","DOI":"10.1007\/978-3-642-61159-9_32"},{"key":"834_CR3","doi-asserted-by":"crossref","unstructured":"Ding C, Zhou D, He X, Zha H (2006) R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In: Proceedings of 23rd international conference on machine learning","DOI":"10.1145\/1143844.1143880"},{"issue":"1","key":"834_CR4","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1109\/TPAMI.2004.1261097","volume":"26","author":"J Yang","year":"2004","unstructured":"Yang J, Zhang D, Frangi A, Yang Y (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans PAMI 26(1):131\u2013137","journal-title":"IEEE Trans PAMI"},{"issue":"1\u20133","key":"834_CR5","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10994-005-3561-6","volume":"61","author":"J Ye","year":"2005","unstructured":"Ye J (2005) Generalized Low rank approximations of matrices. Mach Learn 61(1\u20133):167\u2013191","journal-title":"Mach Learn"},{"key":"834_CR6","unstructured":"De la Torre Fernando, Michael B (2001) Robust principal component analysis for computer vision. In: Proceedings of ICCV, pp. 362-369"},{"issue":"4","key":"834_CR7","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1016\/j.patcog.2009.10.012","volume":"43","author":"Z Liang","year":"2010","unstructured":"Liang Z, Li Y (2010) A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction. Pattern Recognit 43(4):1269\u20131281","journal-title":"Pattern Recognit"},{"issue":"1","key":"834_CR8","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.patcog.2011.07.009","volume":"45","author":"D Meng","year":"2012","unstructured":"Meng D, Zhao Q, Xu Z (2012) Improve robustness of sparse PCA by L1 norm maximization. Pattern Recognit 45(1):487\u2013497","journal-title":"Pattern Recognit"},{"key":"834_CR9","unstructured":"Ke Q, Kanade T (2005) Robust L1 norm factorization in the presence of outliers and missing data by alternative convex programming. In: Proceedings of IEEE conference on computer vision and pattern recognition"},{"issue":"9","key":"834_CR10","doi-asserted-by":"publisher","first-page":"1672","DOI":"10.1109\/TPAMI.2008.114","volume":"30","author":"N Kwak","year":"2009","unstructured":"Kwak N (2009) Principal component analysis based on L1-norm maximization. IEEE Trans Pattern Anal Mach Intell 30(9):1672\u20131680","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"834_CR11","unstructured":"Nie F, Huang H, Ding C, Luo D, Wang H (2011) Robust principal component analysis with non-greedy L1-Norm maximization. In: Proceedings of 22$${nd}$$ international conference on artificial intelligence, pp. 1433\u20131438"},{"issue":"5","key":"834_CR12","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1109\/TCYB.2014.2341575","volume":"45","author":"R Wang","year":"2015","unstructured":"Wang R, Nie F, Yang X, Gao F, Yao M (2015) Robust 2DPCA with non-greedy L1-nom maximization for image analysis. IEEE Trans Cybern 45(5):1108\u20131122","journal-title":"IEEE Trans Cybern"},{"issue":"9","key":"834_CR13","first-page":"1170","volume":"40","author":"X Li","year":"2009","unstructured":"Li X, Pang Y, Yuan Y (2009) L1-norm based 2DPCA. IEEE Trans Syst Man Cybern Part B 40(9):1170\u20131175","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"issue":"2","key":"834_CR14","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1109\/TCSVT.2009.2020337","volume":"20","author":"Y Pang","year":"2010","unstructured":"Pang Y, Li X, Yuan Y (2010) Robust tensor analysis with L1 norm. IEEE Trans Circuits Syst Video Technol 20(2):172\u2013178","journal-title":"IEEE Trans Circuits Syst Video Technol"},{"issue":"8","key":"834_CR15","doi-asserted-by":"publisher","first-page":"3018","DOI":"10.1109\/TIP.2013.2253476","volume":"22","author":"F Zhong","year":"2013","unstructured":"Zhong F, Zhang J (2013) Linear discriminant analysis based on L1 norm maximization. IEEE Trans Image Process 22(8):3018\u20133027","journal-title":"IEEE Trans Image Process"},{"issue":"6","key":"834_CR16","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1109\/TCYB.2013.2273355","volume":"44","author":"H Wang","year":"2014","unstructured":"Wang H, Lu X, Hu Z, Zheng W (2014) Fisher discriminant analysis with L1 norm. IEEE Trans Cybern 44(6):828\u2013842","journal-title":"IEEE Trans Cybern"},{"issue":"11","key":"834_CR17","doi-asserted-by":"publisher","first-page":"2065","DOI":"10.1109\/TNNLS.2014.2303798","volume":"25","author":"F Zhong","year":"2014","unstructured":"Zhong F, Zhang J, Li D (2014) Discriminant locality preserving projections based on L1 norm maximization. IEEE Trans Neural Netw Learn Syst 25(11):2065\u20132074","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"834_CR18","doi-asserted-by":"crossref","unstructured":"Li Z, Tang J, Mei T (2019) Deep collaborative embedding for social image understanding. IEEE Trans PAMI (in press)","DOI":"10.1109\/TPAMI.2018.2852750"},{"issue":"5","key":"834_CR19","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1109\/TCYB.2013.2262936","volume":"44","author":"N Kwak","year":"2015","unstructured":"Kwak N (2015) Principal component analysis based on Lp-norm maximization. IEEE Trans Cybern 44(5):594\u2013609","journal-title":"IEEE Trans Cybern"},{"issue":"9","key":"834_CR20","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1016\/j.patrec.2013.01.030","volume":"34","author":"Z Liang","year":"2013","unstructured":"Liang Z, Xia S, Zhou Y, Zhang L, Li Y (2013) Feature extraction based on Lp norm generalized principal component analysis. Pattern Recognit Lett 34(9):1037\u20131045","journal-title":"Pattern Recognit Lett"},{"issue":"6","key":"834_CR21","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/j.patrec.2013.01.016","volume":"34","author":"J Oh","year":"2013","unstructured":"Oh J, Kwak N (2013) Generalization of linear discriminant analysis using Lp norm. Pattern Recognit Lett 34(6):679\u2013685","journal-title":"Pattern Recognit Lett"},{"issue":"12","key":"834_CR22","first-page":"5345","volume":"24","author":"Z Li","year":"2015","unstructured":"Li Z, Tang J (2015) Unsupervised feature selection via nonnegative spectral analysis and redundancy control. IEEE Trans Image Process 24(12):5345\u20135355","journal-title":"IEEE Trans Image Process"},{"issue":"5","key":"834_CR23","doi-asserted-by":"publisher","first-page":"1947","DOI":"10.1109\/TNNLS.2017.2691725","volume":"29","author":"Z Li","year":"2018","unstructured":"Li Z, Tang J, He X (2018) Robust structured nonnegative matrix factorization for image representation. IEEE Trans Neural Netw Learn Syst 29(5):1947\u20131960","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"10","key":"834_CR24","doi-asserted-by":"publisher","first-page":"2085","DOI":"10.1109\/TPAMI.2015.2400461","volume":"37","author":"Z Li","year":"2015","unstructured":"Li Z, Liu J, Tang J, Hu H (2015) Robust structured subspace learning for data representation. IEEE Trans PAMI 37(10):2085\u20132098","journal-title":"IEEE Trans PAMI"},{"key":"834_CR25","doi-asserted-by":"crossref","unstructured":"Zhao H, Wang Z, Nei F (2019) A new formulation of linear discriminant analysis for robust dimensionality reduction. In: IEEE Transactions on Knowledge and data engineering","DOI":"10.1109\/TKDE.2018.2842023"},{"key":"834_CR26","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.neucom.2012.12.007","volume":"111","author":"Z Liang","year":"2013","unstructured":"Liang Z, Xia S, Zhou Y (2013) Normalized discriminant analysis for dimensionality reduction. Neurocomputing 111:153\u2013159","journal-title":"Neurocomputing"},{"issue":"3","key":"834_CR27","first-page":"38","volume":"27","author":"X He","year":"2005","unstructured":"He X, Yan S, Hu Y, Niyogi P, Zhang HJ (2005) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):38\u2013340","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"2","key":"834_CR28","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch H, Bolte J, Redont P, Soubeyran A (2010) Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka\u2013Lojasiewicz inequality. Math Oper Res 35(2):438\u2013457","journal-title":"Math Oper Res"},{"key":"834_CR29","first-page":"1","volume":"146","author":"J Bolte","year":"2013","unstructured":"Bolte J, Sabach S, Teboulle M (2013) Proximal alternating linearized minimization and projection methods for nonconvex and nonsmooth problems. Math Program 146:1\u201336","journal-title":"Math Program"},{"key":"834_CR30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization, Cambridge","author":"S Boyd","year":"2004","unstructured":"Boyd S, Vandenberghe L (2004) Convex optimization, Cambridge. Cambridge Univ. Press, Cambridge"},{"key":"834_CR31","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/nav.3800030109","volume":"3","author":"M Frank","year":"1956","unstructured":"Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res Logist Q 3:95\u2013110","journal-title":"Naval Res Logist Q"},{"key":"834_CR32","unstructured":"Garber D, Hazan E (2015) Faster rates for the Frank\u2013Wolfe method over strongly-convex sets. In: ICML, pp. 541\u2013549"},{"issue":"1","key":"834_CR33","first-page":"427","volume":"28","author":"M Jaggi","year":"2013","unstructured":"Jaggi M (2013) Revisiting Frank\u2013Wolfe: projection-free sparse convex optimization. ICML 28(1):427\u2013435","journal-title":"ICML"},{"key":"834_CR34","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.ins.2014.03.059","volume":"285","author":"R Nanculef","year":"2014","unstructured":"Nanculef R, Frandi E, Sartori C, Allende H (2014) A novel Frank\u2013Wolfe algorithm. analysis and applications to large-scale SVM training. Inf Sci 285:66\u201399","journal-title":"Inf Sci"},{"issue":"3\u20134","key":"834_CR35","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1561\/2200000050","volume":"8","author":"S Bubeck","year":"2015","unstructured":"Bubeck S (2015) Convex optimization: algorithms and complexity. Found Trends Mach Learn 8(3\u20134):231\u2013358","journal-title":"Found Trends Mach Learn"},{"issue":"5","key":"834_CR36","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1016\/0362-546X(91)90072-9","volume":"16","author":"WH Yang","year":"1991","unstructured":"Yang WH (1991) On generalized holder Inequality. Nonlinear Anal Theory Appl 16(5):489\u2013498","journal-title":"Nonlinear Anal Theory Appl"},{"key":"834_CR37","unstructured":"Liu J, Ye J (2010) Efficient L1\/Lq Norm Regularization, \narXiv:1009.4766v1"},{"key":"834_CR38","doi-asserted-by":"crossref","unstructured":"Sra S (2011) Fast projections onto L1,q-norm balls for grouped feature selection. In: European conference MLKD in databases","DOI":"10.1007\/978-3-642-23808-6_20"},{"issue":"3","key":"834_CR39","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1109\/78.984753","volume":"50","author":"JH Manton","year":"2002","unstructured":"Manton JH (2002) Optimization algorithms exploiting unitary constraints. IEEE Trans Signal Process 50(3):635\u2013650","journal-title":"IEEE Trans Signal Process"},{"key":"834_CR40","volume-title":"Matrix computations","author":"G Golub","year":"1996","unstructured":"Golub G, Loan CV (1996) Matrix computations. Johns Hopkins, Baltimore"},{"key":"834_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-31246-3","volume-title":"Variational analysis and generalized differentiation I basic theory","author":"Boris S Mordukhovich","year":"2006","unstructured":"Mordukhovich Boris S (2006) Variational analysis and generalized differentiation I basic theory. Springer, Berlin"},{"key":"834_CR42","unstructured":"http:\/\/www.can-or.co.uk\/Facedatbase.html"},{"key":"834_CR43","unstructured":"Martines AM, Benavente R (1998) The AR face database. Technical report, CVC"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-019-00834-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10044-019-00834-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-019-00834-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T23:43:33Z","timestamp":1593647013000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10044-019-00834-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,3]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["834"],"URL":"https:\/\/doi.org\/10.1007\/s10044-019-00834-y","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"type":"print","value":"1433-7541"},{"type":"electronic","value":"1433-755X"}],"subject":[],"published":{"date-parts":[[2019,7,3]]},"assertion":[{"value":"22 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}