{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T14:58:22Z","timestamp":1768402702995,"version":"3.49.0"},"reference-count":55,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T00:00:00Z","timestamp":1630022400000},"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":["61772532"],"award-info":[{"award-number":["61772532"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703219"],"award-info":[{"award-number":["61703219"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61976215"],"award-info":[{"award-number":["61976215"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62006232"],"award-info":[{"award-number":["62006232"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20200632"],"award-info":[{"award-number":["BK20200632"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>By combining the broad learning and a convolutional neural network (CNN), a block-diagonal constrained multi-stage convolutional broad learning (MSCBL-BD) method is proposed for hyperspectral image (HSI) classification. Firstly, as the linear sparse feature extracted by the conventional broad learning method cannot fully characterize the complex spatial-spectral features of HSIs, we replace the linear sparse features in the mapped feature (MF) with the features extracted by the CNN to achieve more complex nonlinear mapping. Then, in the multi-layer mapping process of the CNN, information loss occurs to a certain degree. To this end, the multi-stage convolutional features (MSCFs) extracted by the CNN are expanded to obtain the multi-stage broad features (MSBFs). MSCFs and MSBFs are further spliced to obtain multi-stage convolutional broad features (MSCBFs). Additionally, in order to enhance the mutual independence between MSCBFs, a block diagonal constraint is introduced, and MSCBFs are mapped by a block diagonal matrix, so that each feature is represented linearly only by features of the same stage. Finally, the output layer weights of MSCBL-BD and the desired block-diagonal matrix are solved by the alternating direction method of multipliers. Experimental results on three popular HSI datasets demonstrate the superiority of MSCBL-BD.<\/jats:p>","DOI":"10.3390\/rs13173412","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T21:59:45Z","timestamp":1630447185000},"page":"3412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multi-Stage Convolutional Broad Learning with Block Diagonal Constraint for Hyperspectral Image Classification"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1512-0449","authenticated-orcid":false,"given":"Yi","family":"Kong","sequence":"first","affiliation":[{"name":"Engineering Research Center of Intelligent Control for Underground Space, China University of Mining and Technology, Ministry of Education, Xuzhou 221116, China"},{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Xuesong","family":"Wang","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Intelligent Control for Underground Space, China University of Mining and Technology, Ministry of Education, Xuzhou 221116, China"},{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Yuhu","family":"Cheng","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Intelligent Control for Underground Space, China University of Mining and Technology, Ministry of Education, Xuzhou 221116, China"},{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"C. L. Philip","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China"},{"name":"Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau 999078, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2406","DOI":"10.1109\/TCYB.2018.2810806","article-title":"Feature learning using spatial-spectral hypergraph discriminant analysis for hyperspectral image","volume":"49","author":"Luo","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1109\/TCYB.2015.2453359","article-title":"Learning hierarchical spectral-spatial features for hyperspectral image classification","volume":"46","author":"Zhou","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1109\/TGRS.2015.2466438","article-title":"Evaluating NDVI data continuity between SPOT-VEGETATION and PROBA-V missions for operational yield forecasting in North African countries","volume":"54","author":"Meroni","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.1109\/TGRS.2016.2632042","article-title":"A generalized distance transform: Theory and applications to weather analysis and forecasting","volume":"55","author":"Brunet","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1109\/TGRS.2016.2611566","article-title":"A Physics-based algorithm for the simultaneous retrieval of land surface temperature and emissivity from VIIRS thermal infrared data","volume":"55","author":"Islam","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1109\/JSTARS.2015.2417859","article-title":"Hyperspectral tree species classification of Japanese complex mixed forest with the aid of lidar data","volume":"8","author":"Matsuki","year":"2015","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1109\/JSTARS.2017.2768541","article-title":"Hyperspectral image classification with kernel-based least-squares support vector machines in sum space","volume":"11","author":"Liu","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4647","DOI":"10.1109\/JSTARS.2015.2453411","article-title":"GPU parallel implementation of support vector machines for hyperspectral image classification","volume":"8","author":"Tan","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2244672","article-title":"Hyperspectral remote sensing data analysis and future challenges","volume":"1","author":"Plaza","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.isprsjprs.2013.12.003","article-title":"UL-Isomap based nonlinear dimensionality reduction for hyperspectral imagery classification","volume":"89","author":"Sun","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4032","DOI":"10.1109\/TGRS.2017.2686842","article-title":"A sparse and low-rank near-isometric linear embedding method for feature extraction in hyperspectral imagery classification","volume":"55","author":"Sun","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TCYB.2016.2605044","article-title":"Simultaneous spectral-spatial feature selection and extraction for hyperspectral images","volume":"48","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"2604","DOI":"10.1109\/TCYB.2019.2905793","article-title":"Dimensionality reduction of hyperspectral imagery based on spatial-spectral manifold learning","volume":"50","author":"Huang","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6085","DOI":"10.1109\/TGRS.2017.2720584","article-title":"Discriminant analysis of hyperspectral imagery using fast kernel sparse and low-rank graph","volume":"55","author":"Pan","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Pan, L., Li, H., Deng, Y., Zhang, F., Chen, X., 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_18","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1109\/TGRS.2016.2645703","article-title":"Dimensionality reduction and classification of hyperspectral images using ensemble discriminative local metric learning","volume":"55","author":"Dong","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1109\/JSTARS.2016.2587747","article-title":"Exploring locally adaptive dimensionality reduction for hyperspectral image classification: A maximum margin metric learning aspect","volume":"10","author":"Dong","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7140","DOI":"10.1109\/TGRS.2017.2743102","article-title":"PCA-based edge-preserving features for hyperspectral image classification","volume":"55","author":"Kang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/TCYB.2017.2682846","article-title":"A 3-D Gabor phase-based coding and matching framework for hyperspectral imagery classification","volume":"48","author":"Jia","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/TGRS.2011.2162339","article-title":"On combining multiple features for hyperspectral remote sensing image classification","volume":"50","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/TGRS.2014.2345739","article-title":"Multiple feature learning for hyperspectral image classification","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Liu, Z., and Chen, C.L.P. (2017, January 15\u201318). Broad learning system: Structural extensions on single-layer and multi-layer neural networks. Proceedings of the International Conference on Security, Pattern Analysis, and Cybernetics, Shenzhen, China.","DOI":"10.1109\/SPAC.2017.8304264"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/TNNLS.2017.2716952","article-title":"Broad learning system: An effective and efficient incremental learning system without the need for deep architecture","volume":"29","author":"Chen","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1109\/TNNLS.2018.2866622","article-title":"Universal approximation capability of broad learning system and its structural variations","volume":"30","author":"Chen","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/TCYB.2018.2857815","article-title":"Fuzzy broad learning system: A novel neuro-fuzzy model for regression and classification","volume":"50","author":"Feng","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kong, Y., Wang, X., Cheng, Y., and Chen, C.L.P. (2018). Hyperspectral imagery classification based on semi-supervised broad learning system. Remote Sens., 10.","DOI":"10.3390\/rs10050685"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"Lecun","year":"2015","journal-title":"Nature"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MGRS.2016.2540798","article-title":"Deep learning for remote sensing data: A technical tutorial on the state of the art","volume":"4","author":"Zhang","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MGRS.2017.2762307","article-title":"Deep learning in remote sensing: A comprehensive review and list of resources","volume":"5","author":"Zhu","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/TSMC.2018.2884996","article-title":"Hierarchical lifelong learning by sharing representations and integrating hypothesis","volume":"51","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2094","DOI":"10.1109\/JSTARS.2014.2329330","article-title":"Deep learning-based classification of hyperspectral data","volume":"7","author":"Chen","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1109\/JSTARS.2015.2388577","article-title":"Spectral-spatial classification of hyperspectral data based on deep belief network","volume":"8","author":"Chen","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4073","DOI":"10.1109\/JSTARS.2016.2517204","article-title":"Spectral-spatial classification of hyperspectral image based on deep auto-encoder","volume":"9","author":"Ma","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3516","DOI":"10.1109\/TGRS.2017.2675902","article-title":"Learning to diversify deep belief networks for hyperspectral image classification","volume":"55","author":"Zhong","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/LGRS.2016.2630045","article-title":"Deep learning with grouped features for spatial spectral classification of hyperspectral images","volume":"14","author":"Zhou","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1109\/TGRS.2015.2478379","article-title":"Unsupervised deep feature extraction for remote sensing image classification","volume":"54","author":"Romero","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Makantasis, K., Karantzalos, K., Doulamis, A., and Doulamis, N. (2015, January 26\u201331). Deep supervised learning for hyperspectral data classification through convolutional neural networks. Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium, Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326945"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"6232","DOI":"10.1109\/TGRS.2016.2584107","article-title":"Deep feature extraction and classification of hyperspectral images based on convolutional neural networks","volume":"54","author":"Chen","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4544","DOI":"10.1109\/TGRS.2016.2543748","article-title":"Spectral-spatial feature extraction for hyperspectral image classification: A dimension reduction and deep learning approach","volume":"54","author":"Zhao","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1109\/LGRS.2016.2595108","article-title":"A self-improving convolution neural network for the classification of hyperspectral data","volume":"13","author":"Ghamisi","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5293","DOI":"10.1109\/TGRS.2017.2705073","article-title":"BASS net: Band-adaptive spectral-spatial feature learning neural network for hyperspectral image classification","volume":"55","author":"Santara","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5017","DOI":"10.1109\/TIP.2015.2475625","article-title":"PCANet: A simple deep learning baseline for image classification","volume":"24","author":"Chan","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1109\/LGRS.2016.2608963","article-title":"Hyperspectral image classification based on nonlinear spectral-spatial network","volume":"13","author":"Pan","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1109\/JSTARS.2017.2655516","article-title":"R-VCANet: A new deep-learning-based hyperspectral image classification method","volume":"10","author":"Pan","year":"2017","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1109\/TGRS.2016.2616355","article-title":"Hyperspectral image classification using deep pixel-pair features","volume":"55","author":"Li","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.1109\/TNNLS.2014.2339222","article-title":"Dimensionality reduction for hyperspectral data based on class-aware tensor neighborhood graph and patch alignment","volume":"26","author":"Gao","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Sys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1991","DOI":"10.1109\/TITS.2014.2308281","article-title":"Traffic sign recognition with hinge loss trained convolutional neural networks","volume":"15","author":"Jin","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3111","DOI":"10.1109\/TNNLS.2017.2712801","article-title":"Discriminative block-diagonal representation learning for image recognition","volume":"29","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1109\/TGRS.2018.2862899","article-title":"Locality and structure regularized low rank representation for hyperspectral image classification","volume":"57","author":"Wang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4534","DOI":"10.1109\/TCYB.2016.2618852","article-title":"Constrained low-rank representation for robust subspace clustering","volume":"47","author":"Wang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_53","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":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_54","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. Optim."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Vedaldi, A., and Lenc, K. (2014, January 3\u20137). Matconvnet-convolutional neural networks for matlab. Proceedings of the ACM International Conference on Multimedia, Orlando, FL, USA.","DOI":"10.1145\/2733373.2807412"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3412\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:53:49Z","timestamp":1760165629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3412"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,27]]},"references-count":55,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["rs13173412"],"URL":"https:\/\/doi.org\/10.3390\/rs13173412","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,27]]}}}