{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T06:22:34Z","timestamp":1769926954319,"version":"3.49.0"},"reference-count":53,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T00:00:00Z","timestamp":1527120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["No.E2016202341"],"award-info":[{"award-number":["No.E2016202341"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hebei Province Higher Education Institutions","award":["No.BJ2014013"],"award-info":[{"award-number":["No.BJ2014013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Classification of Hyperspectral Images (HSIs) has gained attention for the past few decades. In remote sensing image classification, the labeled samples are insufficient or hard to obtain; however, the unlabeled ones are frequently rich and of a vast number. When there are no sufficient labeled samples, overfitting may occur. To resolve the overfitting issue, in this present work, we proposed a novel approach for HSI feature extraction, called robust regularized Block Low-Rank Discriminant Analysis (BLRDA), which is a robust and efficient feature extraction method to improve the HSIs\u2019 classification accuracy with few labeled samples. To reduce the exponentially growing computational complexity of the low-rank method, we divide the entire image into blocks and implement the low-rank representation for each block respectively. Due to the symmetric matrix requirements for the regularized graph of discriminant analysis, the k-nearest neighbor is applied to handle the whole low-rank graph integrally. The low-rank representation and the kNN can maximally capture and preserve the global and local geometry of the data, respectively, and the performance of regularized discriminant analysis feature extraction can be apparently improved. Extensive experiments on multi-class hyperspectral images show that the proposed BLRDA is a very robust and efficient feature extraction method. Even with simple supervised and semi-supervised classifiers (nearest neighbor and SVM) and randomly given parameters, the feature extraction method achieves significant results with few labeled samples, which shows better performance than similar feature extraction methods.<\/jats:p>","DOI":"10.3390\/rs10060817","type":"journal-article","created":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T07:54:01Z","timestamp":1527148441000},"page":"817","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Classification of Hyperspectral Images with Robust Regularized Block Low-Rank Discriminant Analysis"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7070-831X","authenticated-orcid":false,"given":"Baokai","family":"Zu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Hebei University of Technology, Tianjin 300401, China"},{"name":"Computer Science Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kewen","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Du","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Huazhong Agricultural University, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yafang","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6308-741X","authenticated-orcid":false,"given":"Ahmad","family":"Ali","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sagnik","family":"Chakraborty","sequence":"additional","affiliation":[{"name":"Post Doctoral Fellow, School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xu, L., Zhang, H., Zhao, M., Chu, D., and Li, Y. (2017, January 22\u201325). Integrating Spectral and Spatial Features for Hyperspectral Image Classification Using Low-Rank Representation. Proceedings of the IEEE International Conference on Industrial Technology (ICIT), Toronto, ON, Canada.","DOI":"10.1109\/ICIT.2017.7915502"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.rse.2003.12.013","article-title":"Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture","volume":"90","author":"Haboudane","year":"2004","journal-title":"Remote Sens. Environ."},{"key":"ref_3","first-page":"165","article-title":"A review on reflective remote sensing and data assimilation techniques for enhanced agroecosystem modeling","volume":"9","author":"Dorigo","year":"2007","journal-title":"Int. J. Appl. Earth Obs. Geoinform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1016\/j.rse.2009.06.013","article-title":"The role of spectral resolution and classifier complexity in the analysis of hyperspectral images of forest areas","volume":"113","author":"Dalponte","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_5","first-page":"523","article-title":"Using imaging spectroscopy to study ecosystem processes and properties","volume":"54","author":"Ustin","year":"2004","journal-title":"AIBS Bull."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/36.911111","article-title":"Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery","volume":"39","author":"Heinz","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1109\/TGRS.2003.812908","article-title":"Comparison of airborne hyperspectral data and EO-1 Hyperion for mineral mapping","volume":"41","author":"Kruse","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","unstructured":"Cocks, T., Jenssen, R., Stewart, A., Wilson, I., and Shields, T. (1998, January 6\u20138). The HyMapTM Airborne Hyperspectral Sensor: The System, Calibration and Performance. Proceedings of the 1st EARSeL workshop on Imaging Spectroscopy, Zurich, Switzerland."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3410","DOI":"10.1109\/TGRS.2016.2517242","article-title":"Kernel low-rank and sparse graph for unsupervised and semi-supervised classification of hyperspectral images","volume":"54","author":"Borgeaud","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TIT.1968.1054102","article-title":"On the mean accuracy of statistical pattern recognizers","volume":"14","author":"Hughes","year":"1968","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear dimensionality reduction by locally linear embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A global geometric framework for nonlinear dimensionality reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","article-title":"Laplacian eigenmaps for dimensionality reduction and data representation","volume":"15","author":"Belkin","year":"2003","journal-title":"Neural Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2287","DOI":"10.1109\/TGRS.2011.2172617","article-title":"A fast and robust sparse approach for hyperspectral data classification using a few labeled samples","volume":"50","author":"Tao","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1109\/TGRS.2006.885074","article-title":"Feature extractions for small sample size classification problem","volume":"45","author":"Kuo","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2739","DOI":"10.1109\/JSTARS.2014.2362116","article-title":"Multiple kernel learning via low-rank nonnegative matrix factorization for classification of hyperspectral imagery","volume":"8","author":"Gu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3742","DOI":"10.1109\/TGRS.2013.2275613","article-title":"Feature extraction of hyperspectral images with image fusion and recursive filtering","volume":"52","author":"Kang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","unstructured":"Zhou, D., Bousquet, O., Lal, T.N., Weston, J., and Sch\u00f6lkopf, B. (2004). Learning with local and global consistency. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Guo, Z., Zhang, Z., Xing, E.P., and Faloutsos, C. (2008, January 24\u201326). Semi-Supervised Learning based on Semiparametric Regularization. Proceedings of the SIAM International Conference on Data Mining, Atlanta, Georgia.","DOI":"10.1137\/1.9781611972788.12"},{"key":"ref_20","first-page":"1","article-title":"Graph-based semi-supervised learning","volume":"8","author":"Subramanya","year":"2014","journal-title":"Synth. Lect. Artif. Intell. Mach. Learn."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cai, D., He, X., and Han, J. (2007, January 14\u201320). Semi-Supervised Discriminant Analysis. Proceedings of the IEEE 11th International Conference on Computer Vision, Rio de Janeiro, Brazil.","DOI":"10.1109\/ICCV.2007.4408856"},{"key":"ref_22","unstructured":"Jebara, T., Wang, J., and Chang, S.F. (2009, January 14\u201318). Graph Construction and b-Matching for Semi-Supervised Learning. Proceedings of the 26th Annual International Conference on Machine Learning, Montreal, QC, Canada."},{"key":"ref_23","unstructured":"Yan, S., and Wang, H. (May, January 30). Semi-supervised Learning by Sparse Representation. Proceedings of the SIAM International Conference on Data Mining, Sparks, NV, USA."},{"key":"ref_24","unstructured":"Zhu, X., Lafferty, J., and Rosenfeld, R. (2005). Semi-Supervised Learning with Graphs. [Ph.D. Thesis, Carnegie Mellon University]."},{"key":"ref_25","unstructured":"Zhu, X., Ghahramani, Z., and Lafferty, J.D. (2003, January 21\u201324). Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions. Proceedings of the 20th International Conference on Machine Learning (ICML-03), Washington, DC, USA."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Belkin, M., Matveeva, I., and Niyogi, P. (2004). Regularization and semi-supervised learning on large graphs. International Conference on Computational Learning Theory, Springer.","DOI":"10.1007\/978-3-540-27819-1_43"},{"key":"ref_27","unstructured":"Zhuang, L., Gao, H., Lin, Z., Ma, Y., Zhang, X., and Yu, N. (2012, January 16\u201321). Non-Negative Low Rank and Sparse Graph for Semi-Supervised Learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Providence, RI, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3717","DOI":"10.1109\/TIP.2015.2441632","article-title":"Constructing a nonnegative low-rank and sparse graph with data-adaptive features","volume":"24","author":"Zhuang","year":"2015","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_29","unstructured":"Liu, G., Lin, Z., and Yu, Y. (2010, January 21\u201325). Robust Subspace Segmentation by Low-Rank Representation. Proceedings of the 27th International Conference on Machine Learning (ICML-10), Haifa, Israel."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4094","DOI":"10.1109\/TGRS.2016.2536685","article-title":"Sparse and Low-Rank Graph for Discriminant Analysis of Hyperspectral Imagery","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.patcog.2011.09.001","article-title":"Supervised neighborhood graph construction for semi-supervised classification","volume":"45","author":"Rohban","year":"2012","journal-title":"Patt. Recognit."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1109\/TGRS.2013.2284280","article-title":"Hyperspectral image restoration using low-rank matrix recovery","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/TIP.2015.2496263","article-title":"Hyperspectral super-resolution of locally low-rank images from complementary multisource data","volume":"25","author":"Veganzones","year":"2016","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Niu, Y., and Wang, B. (2016). Hyperspectral Anomaly Detection Based on Low-Rank Representation and Learned Dictionary. Remote Sens., 8.","DOI":"10.3390\/rs8040289"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Pan, L., Li, H.C., Deng, Y.J., Zhang, F., Chen, X.D., and Du, Q. (2017). Hyperspectral Dimensionality Reduction by Tensor Sparse and Low-Rank Graph-Based Discriminant Analysis. Remote Sens., 9.","DOI":"10.3390\/rs9050452"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TGRS.2015.2452812","article-title":"Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration","volume":"54","author":"He","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Qi, K., Liu, W., Yang, C., Guan, Q., and Wu, H. (2016). Multi-Task Joint Sparse and Low-Rank Representation for the Scene Classification of High-Resolution Remote Sensing Image. Remote Sens., 9.","DOI":"10.3390\/rs9010010"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zu, B., Xia, K., Pan, Y., and Niu, W. (2017). A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and-Nearest Neighbor Graph. Comput. Intell. Neurosci., 2017.","DOI":"10.1155\/2017\/9290230"},{"key":"ref_39","first-page":"305","article-title":"On transductive regression","volume":"19","author":"Cortes","year":"2007","journal-title":"Adv. Neural Inf. Proc. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhang, L., Wei, W., Zhang, Y., Shen, C., van den Hengel, A., and Shi, Q. (2016). Cluster sparsity field for hyperspectral imagery denoising. European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-319-46454-1_38"},{"key":"ref_41","first-page":"11","article-title":"Robust principal component analysis?","volume":"58","author":"Li","year":"2011","journal-title":"J. ACM (JACM)"},{"key":"ref_42","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":"2010","journal-title":"SIAM J. Opt."},{"key":"ref_43","unstructured":"Lin, Z., Chen, M., and Ma, Y. (arXiv, 2010). The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices, arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","article-title":"Robust recovery of subspace structures by low-rank representation","volume":"35","author":"Liu","year":"2013","journal-title":"Patt. Anal. Mach. Intell. IEEE Trans."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1145\/2010324.1964964","article-title":"Domain transform for edge-aware image and video processing","volume":"Volume 30","author":"Gastal","year":"2011","journal-title":"ACM Transactions on Graphics (ToG)"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0034-4257(91)90048-B","article-title":"A review of assessing the accuracy of classifications of remotely sensed data","volume":"37","author":"Congalton","year":"1991","journal-title":"Remote Sens. Environ."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Richards, J.A., and Richards, J. (1999). Remote Sensing Digital Image Analysis, Springer.","DOI":"10.1007\/978-3-662-03978-6"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/0895-4356(88)90031-5","article-title":"A reappraisal of the kappa coefficient","volume":"41","author":"Thompson","year":"1988","journal-title":"J. Clin. Epidemiol."},{"key":"ref_49","first-page":"1","article-title":"Kappa statistic is not satisfactory for assessing the extent of agreement between raters","volume":"1","author":"Gwet","year":"2002","journal-title":"Stat. Methods Int. Reliab. Assess."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Javed, M.A., Younis, M.S., Latif, S., Qadir, J., and Baig, A. (2018). Community detection in networks: A multidisciplinary review. J. Netw. Comput. Appl.","DOI":"10.1016\/j.jnca.2018.02.011"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TBDATA.2016.2631512","article-title":"An empirical comparison of algorithms to find communities in directed graphs and their application in web data analytics","volume":"3","author":"Agreste","year":"2017","journal-title":"IEEE Trans. Big Data"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.ins.2017.10.019","article-title":"Hidden community detection in social networks","volume":"425","author":"He","year":"2017","journal-title":"Inf. Sci. Int. J."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Nathan, E., Zakrzewska, A., Riedy, J., and Bader, D.A. (2017). Local Community Detection in Dynamic Graphs Using Personalized Centrality. Algorithms, 10.","DOI":"10.3390\/a10030102"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/817\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:05:45Z","timestamp":1760195145000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/817"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,24]]},"references-count":53,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["rs10060817"],"URL":"https:\/\/doi.org\/10.3390\/rs10060817","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,24]]}}}