{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T04:17:37Z","timestamp":1749615457317,"version":"3.41.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,10,7]],"date-time":"2016-10-07T00:00:00Z","timestamp":1475798400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2016,10,7]],"date-time":"2016-10-07T00:00:00Z","timestamp":1475798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61373055"],"award-info":[{"award-number":["61373055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013286","name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"crossref","award":["20130093110009"],"award-info":[{"award-number":["20130093110009"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Adapt Syst Model"],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we propose a novel method for semi-supervised learning by combining graph embedding and sparse regression, termed as graph embedding and sparse regression with structure low rank representation (GESR-LR), in which the embedding learning and the sparse regression are performed in a combined approach. Most of the graph based semi-supervised learning methods take into account the local neighborhood information while ignoring the global structure of the data. The proposed GESR-LR method learns a low-rank weight matrix by projecting the data onto a low-dimensional subspace. The GESR-LR makes full use of the supervised learning information in the construction of the affinity matrix, and the affinity construction is combined with graph embedding in a single step to guarantee the global optimal solution. In the dimensionality reduction procedure, the proposed GESR-LR can preserve the global structure of the data, and the learned low-rank weight matrix can effectively reduce the influence of the noise. An effective novel algorithm to solve the corresponding optimization problem was designed and is presented in this paper. Extensive experimental results demonstrate that the GESR-LR method can obtain a higher classification accuracy than other state-of-the-art methods.<\/jats:p>","DOI":"10.1186\/s40294-016-0034-7","type":"journal-article","created":{"date-parts":[[2016,10,7]],"date-time":"2016-10-07T12:05:49Z","timestamp":1475841949000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Combining graph embedding and sparse regression with structure low-rank representation for semi-supervised learning"],"prefix":"10.1186","volume":"4","author":[{"given":"Cong-Zhe","family":"You","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vasile","family":"Palade","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Jun","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,10,7]]},"reference":[{"issue":"7","key":"34_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(7):711\u2013720","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"6","key":"34_CR2","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M Belkin","year":"2003","unstructured":"Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373\u20131396","journal-title":"Neural Comput"},{"issue":"7","key":"34_CR3","first-page":"2399","volume":"1","author":"M Belkin","year":"2006","unstructured":"Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 1(7):2399\u20132434","journal-title":"J Mach Learn Res"},{"key":"34_CR4","doi-asserted-by":"crossref","unstructured":"Cai D, He X, Han J (2007) Semi-supervised discriminant analysis. In: IEEE 11th international conference on computer vision, 2007, ICCV 2007. IEEE, New York, pp 1\u20137","DOI":"10.1109\/ICCV.2007.4408856"},{"issue":"3","key":"34_CR5","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1145\/1970392.1970395","volume":"58","author":"EJ Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis? J ACM 58(3):11","journal-title":"J ACM"},{"key":"34_CR6","unstructured":"Goldberger J, Hinton GE, Roweis ST, Salakhutdinov R (2004) Neighborhood components analysis. In: Advances in neural information processing systems, pp 513\u2013520"},{"issue":"3","key":"34_CR7","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1109\/TPAMI.2005.55","volume":"27","author":"X He","year":"2005","unstructured":"He X, Yan S, Hu Y, Niyogi P, Zhang HJ (2005a) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328\u2013340","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"34_CR8","doi-asserted-by":"crossref","unstructured":"He X, Cai D, Yan S, Zhang HJ (2005b) Neighborhood preserving embedding. In: Tenth IEEE international conference on computer vision, 2005. ICCV 2005, vol 2. IEEE, New York, pp 1208\u20131213","DOI":"10.1109\/ICCV.2005.167"},{"key":"34_CR9","doi-asserted-by":"crossref","unstructured":"Holland, John H (2012) Signals and boundaries: building blocks for complex adaptive systems. Mit Press, Cambridge","DOI":"10.7551\/mitpress\/9412.001.0001"},{"issue":"2","key":"34_CR10","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1109\/TSMCB.2007.914706","volume":"38","author":"X Li","year":"2008","unstructured":"Li X, Lin S, Yan S, Xu D (2008) Discriminant locally linear embedding with high-order tensor data. IEEE Trans Syst Man Cybern Part B 38(2):342\u2013352","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"key":"34_CR11","doi-asserted-by":"crossref","unstructured":"Liu W, Tao D, Liu J (2008) Transductive component analysis. In: Eighth IEEE international conference on data mining, 2008, ICDM\u201908. IEEE, New York, pp 433\u2013442","DOI":"10.1109\/ICDM.2008.101"},{"key":"34_CR12","unstructured":"Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: ICML, pp 663\u2013670"},{"issue":"1","key":"34_CR13","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","volume":"35","author":"G Liu","year":"2013","unstructured":"Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171\u2013184","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"34_CR14","first-page":"21","volume-title":"Complex adaptive systems. Cognitive agent-based computing-I","author":"Muaz A Niazi","year":"2013","unstructured":"Niazi Muaz A, Hussain Amir (2013) Complex adaptive systems. Cognitive agent-based computing-I. Springer, Amsterdam, pp 21\u201332"},{"issue":"11","key":"34_CR15","doi-asserted-by":"publisher","first-page":"2615","DOI":"10.1016\/j.patcog.2009.04.001","volume":"42","author":"F Nie","year":"2009","unstructured":"Nie F, Xiang S, Jia Y, Zhang C (2009) Semi-supervised orthogonal discriminant analysis via label propagation. Pattern Recogn 42(11):2615\u20132627","journal-title":"Pattern Recogn"},{"issue":"7","key":"34_CR16","doi-asserted-by":"publisher","first-page":"1921","DOI":"10.1109\/TIP.2010.2044958","volume":"19","author":"F Nie","year":"2010","unstructured":"Nie F, Xu D, Tsang IW, Zhang C (2010) Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction. IEEE Trans Image Process 19(7):1921\u20131932","journal-title":"IEEE Trans Image Process"},{"issue":"3","key":"34_CR17","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1109\/TSMCB.2010.2085433","volume":"41","author":"F Nie","year":"2011","unstructured":"Nie F, Xu D, Li X, Xiang S (2011) Semi-supervised dimensionality reduction and classification through virtual label regression. IEEE Trans Syst Man Cybern Part B 41(3):675\u2013685","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"key":"34_CR18","unstructured":"Nie F, Yuan J, Huang H (2014) Optimal mean robust principal component analysis. In: Proceedings of the 31st international conference on machine learning (ICML-14), pp 1062\u20131070"},{"issue":"5500","key":"34_CR19","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323\u20132326","journal-title":"Science"},{"issue":"5500","key":"34_CR20","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum JB, De Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319\u20132323","journal-title":"Science"},{"issue":"2","key":"34_CR21","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1109\/TIP.2013.2297020","volume":"23","author":"SJ Wang","year":"2014","unstructured":"Wang SJ, Yan S, Yang J, Zhou CG, Fu X (2014) A general exponential framework for dimensionality reduction. IEEE Trans Image Process 23(2):920\u2013930","journal-title":"IEEE Trans Image Process"},{"key":"34_CR22","unstructured":"Wright J, Ganesh A, Rao S, Peng Y, Ma Y (2009) Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Advances in neural information processing systems, pp 2080\u20132088"},{"key":"34_CR23","doi-asserted-by":"crossref","unstructured":"Wu M, Yu K, Yu S, Sch\u00f6lkopf B (2007) Local learning projections. In: Proceedings of the 24th international conference on machine learning. ACM, New York, pp 1039\u20131046","DOI":"10.1145\/1273496.1273627"},{"issue":"10","key":"34_CR24","doi-asserted-by":"publisher","first-page":"1913","DOI":"10.1109\/TPAMI.2009.51","volume":"31","author":"D Xu","year":"2009","unstructured":"Xu D, Yan S, Lin S, Huang TS, Chang SF (2009) Enhancing bilinear subspace learning by element rearrangement. IEEE Trans Pattern Anal Mach Intell 31(10):1913\u20131920","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"34_CR25","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/TPAMI.2007.250598","volume":"29","author":"S Yan","year":"2007","unstructured":"Yan S, Xu D, Zhang B, Zhang HJ, Yang Q, Lin S (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40\u201351","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"10","key":"34_CR26","doi-asserted-by":"publisher","first-page":"2761","DOI":"10.1109\/TIP.2010.2049235","volume":"19","author":"Y Yang","year":"2010","unstructured":"Yang Y, Xu D, Nie F, Yan S, Zhuang Y (2010) Image clustering using local discriminant models and global integration. IEEE Trans Image Process 19(10):2761\u20132773","journal-title":"IEEE Trans Image Process"},{"issue":"7","key":"34_CR27","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1109\/TNNLS.2013.2249088","volume":"24","author":"J Yang","year":"2013","unstructured":"Yang J, Chu D, Zhang L, Xu Y, Yang J (2013) Sparse representation classifier steered discriminative projection with applications to face recognition. IEEE Trans Neural Networks Learn Syst 24(7):1023\u20131035","journal-title":"IEEE Trans Neural Networks Learn Syst"},{"issue":"9","key":"34_CR28","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1109\/TKDE.2008.212","volume":"21","author":"T Zhang","year":"2009","unstructured":"Zhang T, Tao D, Li X, Yang J (2009) Patch alignment for dimensionality reduction. IEEE Trans Knowl Data Eng 21(9):1299\u20131313","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"4","key":"34_CR29","doi-asserted-by":"publisher","first-page":"1684","DOI":"10.1109\/TSP.2011.2179539","volume":"60","author":"L Zhang","year":"2012","unstructured":"Zhang L, Zhou WD, Chang PC, Liu J, Yan Z, Wang T, Li FZ (2012) Kernel sparse representation-based classifier. IEEE Trans Signal Process 60(4):1684\u20131695","journal-title":"IEEE Trans Signal Process"},{"issue":"1","key":"34_CR30","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1109\/TIP.2012.2202678","volume":"22","author":"T Zhou","year":"2013","unstructured":"Zhou T, Tao D (2013) Double shrinking sparse dimension reduction. IEEE Trans Image Process 22(1):244\u2013257","journal-title":"IEEE Trans Image Process"},{"issue":"16","key":"34_CR31","first-page":"321","volume":"16","author":"D Zhou","year":"2004","unstructured":"Zhou D, Bousquet O, Lal TN, Weston J, Sch\u00f6lkopf B (2004) Learning with local and global consistency. Adv Neural Inform Process Syst 16(16):321\u2013328","journal-title":"Adv Neural Inform Process Syst"},{"key":"34_CR32","unstructured":"Zhu X, Ghahramani Z, Lafferty J (2003) Semi-supervised learning using Gaussian fields and harmonic functions. In: ICML, vol 3, pp. 912\u2013919"},{"key":"34_CR33","doi-asserted-by":"crossref","unstructured":"Zhuang L, Gao H, Lin Z, Ma Y, Zhang X, Yu N (2012) Non-negative low rank and sparse graph for semi-supervised learning. In: IEEE conference on computer vision and pattern recognition (CVPR), 2012. IEEE, New York, pp 2328\u20132335","DOI":"10.1109\/CVPR.2012.6247944"},{"issue":"4","key":"34_CR34","doi-asserted-by":"publisher","first-page":"946","DOI":"10.1109\/TSMCB.2005.863377","volume":"36","author":"W Zuo","year":"2006","unstructured":"Zuo W, Zhang D, Yang J, Wang K (2006) BDPCA plus LDA: a novel fast feature extraction technique for face recognition. IEEE Trans Syst Man Cybern Part B 36(4):946\u2013953","journal-title":"IEEE Trans Syst Man Cybern Part B"}],"container-title":["Complex Adaptive Systems Modeling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40294-016-0034-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40294-016-0034-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40294-016-0034-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T02:53:17Z","timestamp":1749610397000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s40294-016-0034-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,7]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["34"],"URL":"https:\/\/doi.org\/10.1186\/s40294-016-0034-7","relation":{},"ISSN":["2194-3206"],"issn-type":[{"type":"electronic","value":"2194-3206"}],"subject":[],"published":{"date-parts":[[2016,10,7]]},"assertion":[{"value":"8 August 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 October 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"22"}}