{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:12:52Z","timestamp":1760235172600,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"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":["61903279, 61773295, 61906140"],"award-info":[{"award-number":["61903279, 61773295, 61906140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China - Civil Aviation Administration of China","award":["U1833119"],"award-info":[{"award-number":["U1833119"]}]},{"name":"Hubei Natural Science Foundation for Distinguished Young Scholars","award":["2020CFA063"],"award-info":[{"award-number":["2020CFA063"]}]},{"name":"National Food and Strategic Reserves Administration Foundation","award":["LQ2018501"],"award-info":[{"award-number":["LQ2018501"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The representation-based algorithm has raised a great interest in hyperspectral image (HSI) classification. l1-minimization-based sparse representation (SR) attempts to select a few atoms and cannot fully reflect within-class information, while l2-minimization-based collaborative representation (CR) tries to use all of the atoms leading to mixed-class information. Considering the above problems, we propose the pairwise elastic net representation-based classification (PENRC) method. PENRC combines the l1-norm and l2-norm penalties and introduces a new penalty term, including a similar matrix between dictionary atoms. This similar matrix enables the automatic grouping selection of highly correlated data to estimate more robust weight coefficients for better classification performance. To reduce computation cost and further improve classification accuracy, we use part of the atoms as a local adaptive dictionary rather than the entire training atoms. Furthermore, we consider the neighbor information of each pixel and propose a joint pairwise elastic net representation-based classification (J-PENRC) method. Experimental results on chosen hyperspectral data sets confirm that our proposed algorithms outperform the other state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/e23080956","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T22:22:46Z","timestamp":1627338166000},"page":"956","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Pairwise Elastic Net Representation-Based Classification for Hyperspectral Image Classification"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2769-4842","authenticated-orcid":false,"given":"Hao","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanshu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Ma","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoguang","family":"Mei","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaqin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bykov, A., Zherebtsov, E., Dremin, V., Popov, A., Doronin, A., and Meglinski, I. (2019). Hyperspecral Skin Imaging with Artificial Neural Networks Validated by Optical Biotissue Phantoms. Proceedings of the Computational Optical Sensing and Imaging, Munich, Germany, 24\u201327 June 2019, Optical Society of America.","DOI":"10.1364\/COSI.2019.CW1A.3"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1552","DOI":"10.1109\/TGRS.2004.830549","article-title":"Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries","volume":"42","author":"Keshava","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2409","DOI":"10.1080\/01431161003698336","article-title":"Hyperspectral remote sensing for mineral exploration in Pulang, Yunnan Province, China","volume":"32","author":"Bishop","year":"2011","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1109\/TGRS.2004.831865","article-title":"Classification of hyperspectral remote sensing images with support vector machines","volume":"42","author":"Melgani","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3399","DOI":"10.1109\/TGRS.2013.2272760","article-title":"Decision fusion in kernel-induced spaces for hyperspectral image classification","volume":"52","author":"Li","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TGRS.2011.2165957","article-title":"Locality-preserving dimensionality reduction and classification for hyperspectral image analysis","volume":"50","author":"Li","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1016\/j.ins.2020.09.009","article-title":"Locality-constrained sparse representation for hyperspectral image classification","volume":"546","author":"Zhang","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2672","DOI":"10.1109\/TNNLS.2018.2885616","article-title":"Learning a low tensor-train rank representation for hyperspectral image super-resolution","volume":"30","author":"Dian","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TCI.2019.2911881","article-title":"Deep spatial\u2013spectral representation learning for hyperspectral image denoising","volume":"5","author":"Dong","year":"2019","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sellami, A., Dup\u00e9, F.X., Cagna, B., Kadri, H., Ayache, S., Arti\u00e8res, T., and Takerkart, S. (2020, January 19\u201324). Mapping individual differences in cortical architecture using multi-view representation learning. Proceedings of the 2020 International Joint Conference on Neural Networks (IJCNN), Glasgow, UK.","DOI":"10.1109\/IJCNN48605.2020.9206887"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MGRS.2018.2854840","article-title":"New frontiers in spectral-spatial hyperspectral image classification: The latest advances based on mathematical morphology, Markov random fields, segmentation, sparse representation, and deep learning","volume":"6","author":"Ghamisi","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sellami, A., and Farah, I. (2019, January 17\u201320). Spectra-spatial graph-based deep restricted boltzmann networks for hyperspectral image classification. Proceedings of the 2019 PhotonIcs & Electromagnetics Research Symposium-Spring (PIERS-Spring), Rome, Italy.","DOI":"10.1109\/PIERS-Spring46901.2019.9017309"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Mei, X., Pan, E., Ma, Y., Dai, X., Huang, J., Fan, F., Du, Q., Zheng, H., and Ma, J. (2019). Spectral-spatial attention networks for hyperspectral image classification. Remote Sens., 11.","DOI":"10.3390\/rs11080963"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lei, Z., Zeng, Y., Liu, P., and Su, X. (2021). Active deep learning for hyperspectral image classification with uncertainty learning. IEEE Geosci. Remote Sens. Lett.","DOI":"10.1109\/LGRS.2020.3045437"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/LGRS.2016.2532380","article-title":"Hyperspectral image classification with robust sparse representation","volume":"13","author":"Li","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7770","DOI":"10.1109\/TGRS.2019.2916329","article-title":"Collaborative representation-based multiscale superpixel fusion for hyperspectral image classification","volume":"57","author":"Jia","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3973","DOI":"10.1109\/TGRS.2011.2129595","article-title":"Hyperspectral image classification using dictionary-based sparse representation","volume":"49","author":"Chen","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/TGRS.2013.2241773","article-title":"Nearest regularized subspace for hyperspectral classification","volume":"52","author":"Li","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2683","DOI":"10.1109\/TGRS.2014.2363582","article-title":"Class-dependent sparse representation classifier for robust hyperspectral image classification","volume":"53","author":"Cui","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","unstructured":"Zhang, L., Yang, M., and Feng, X. (2011, January 6\u201313). Sparse representation or collaborative representation: Which helps face recognition?. Proceedings of the 2011 International Conference on Computer Vision, Barcelona, Spain."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1109\/JSTARS.2014.2306956","article-title":"Joint within-class collaborative representation for hyperspectral image classification","volume":"7","author":"Li","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/LGRS.2014.2325978","article-title":"Kernel collaborative representation with Tikhonov regularization for hyperspectral image classification","volume":"12","author":"Li","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3707","DOI":"10.1109\/TGRS.2013.2274875","article-title":"Hyperspectral image classification by nonlocal joint collaborative representation with a locally adaptive dictionary","volume":"52","author":"Li","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/JSTARS.2015.2477364","article-title":"Hyperspectral image classification via shape-adaptive joint sparse representation","volume":"9","author":"Fu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4178","DOI":"10.1109\/JSTARS.2016.2542113","article-title":"Hyperspectral image classification by fusing collaborative and sparse representations","volume":"9","author":"Li","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1111\/j.1467-9868.2005.00527.x","article-title":"Regularization and variable selection via the elastic net","volume":"67","author":"Hui","year":"2005","journal-title":"J. R. Stat. Soc."},{"key":"ref_27","unstructured":"Lorbert, A., Eis, D., Kostina, V., Blei, D., and Ramadge, P. (2010, January 13\u201315). Exploiting covariate similarity in sparse regression via the pairwise elastic net. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, Sardinia, Italy."},{"key":"ref_28","unstructured":"Chen, S., and Donoho, D. (November, January 31). Basis pursuit. Proceedings of the 1994 28th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4595","DOI":"10.1109\/TSP.2011.2161292","article-title":"The in-crowd algorithm for fast basis pursuit denoising","volume":"59","author":"Gill","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching pursuits with time-frequency dictionaries","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/JSTARS.2012.2194696","article-title":"Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches","volume":"5","author":"Plaza","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Huang, S., Zhang, H., and Pi\u017eurica, A. (2017). A robust sparse representation model for hyperspectral image classification. Sensors, 17.","DOI":"10.3390\/s17092087"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7738","DOI":"10.1109\/TGRS.2014.2318058","article-title":"Spectral\u2013spatial hyperspectral image classification via multiscale adaptive sparse representation","volume":"52","author":"Fang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1109\/TGRS.2008.2005729","article-title":"Classification of hyperspectral images with regularized linear discriminant analysis","volume":"47","author":"Bandos","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1214\/07-AOAS131","article-title":"Pathwise coordinate optimization","volume":"1","author":"Friedman","year":"2007","journal-title":"Ann. Appl. Stat."},{"key":"ref_36","first-page":"4099","article-title":"Local manifold learning-based k-nearest-neighbor for hyperspectral image classification","volume":"48","author":"Ma","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4063","DOI":"10.1109\/JSTARS.2018.2869376","article-title":"Hyperspectral image classification via weighted joint nearest neighbor and sparse representation","volume":"11","author":"Tu","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_38","first-page":"221","article-title":"Support vector machines for hyperspectral remote sensing classification","volume":"Volume 3584","author":"Gualtieri","year":"1999","journal-title":"Proceedings of the 27th AIPR Workshop: Advances in Computer-Assisted Recognition, Washington, DC, USA, 14\u201316 October 1999"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4995","DOI":"10.1109\/JSTARS.2019.2949621","article-title":"Multifeature-Based Discriminative Label Consistent K-SVD for Hyperspectral Image Classification","volume":"12","author":"Ma","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_40","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"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/956\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:35:16Z","timestamp":1760164516000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/956"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,26]]},"references-count":40,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23080956"],"URL":"https:\/\/doi.org\/10.3390\/e23080956","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,7,26]]}}}