{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T00:05:47Z","timestamp":1785801947882,"version":"3.56.0"},"reference-count":41,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,11,13]],"date-time":"2017-11-13T00:00:00Z","timestamp":1510531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a new machine learning approach, the extreme learning machine (ELM) has received much attention due to its good performance. However, when directly applied to hyperspectral image (HSI) classification, the recognition rate is low. This is because ELM does not use spatial information, which is very important for HSI classification. In view of this, this paper proposes a new framework for the spectral-spatial classification of HSI by combining ELM with loopy belief propagation (LBP). The original ELM is linear, and the nonlinear ELMs (or Kernel ELMs) are an improvement of linear ELM (LELM). However, based on lots of experiments and much analysis, it is found that the LELM is a better choice than nonlinear ELM for the spectral-spatial classification of HSI. Furthermore, we exploit the marginal probability distribution that uses the whole information in the HSI and learns such a distribution using the LBP. The proposed method not only maintains the fast speed of ELM, but also greatly improves the accuracy of classification. The experimental results in the well-known HSI data sets, Indian Pines, and Pavia University, demonstrate the good performance of the proposed method.<\/jats:p>","DOI":"10.3390\/s17112603","type":"journal-article","created":{"date-parts":[[2017,11,13]],"date-time":"2017-11-13T11:12:36Z","timestamp":1510571556000},"page":"2603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Linear vs. Nonlinear Extreme Learning Machine for Spectral-Spatial Classification of Hyperspectral Images"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0281-6092","authenticated-orcid":false,"given":"Faxian","family":"Cao","sequence":"first","affiliation":[{"name":"School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8336-5109","authenticated-orcid":false,"given":"Zhijing","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinchang","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengying","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wing-Kuen","family":"Ling","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1109\/TGRS.2014.2333539","article-title":"Dimension reduction using spatial and spectral regularized local discriminant embedding for hyperspectral image classification","volume":"53","author":"Zhou","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1109\/TGRS.2012.2205263","article-title":"Spectral\u2013spatial classification of hyperspectral data using loopy belief propagation and active learning","volume":"51","author":"Li","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2015.11.044","article-title":"Novel segmented stacked autoencoder for effective dimensionality reduction and feature extraction in hyperspectral imaging","volume":"185","author":"Zabalza","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/MSP.2014.2312071","article-title":"Effective feature extraction and data reduction with hyperspectral imaging in remote sensing","volume":"31","author":"Ren","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1109\/TGRS.2016.2598065","article-title":"Effective denoising and classification of hyperspectral images using curvelet transform and singular spectrum analysis","volume":"55","author":"Qiao","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4418","DOI":"10.1109\/TGRS.2015.2398468","article-title":"Novel two dimensional singular spectrum analysis for effective feature extraction and data classification in hyperspectral imaging","volume":"53","author":"Zabalza","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.compag.2015.05.007","article-title":"Singular spectrum analysis for improving hyperspectral imaging based beef eating quality evaluation","volume":"115","author":"Qiao","year":"2015","journal-title":"Comput. Electron. Agric."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2845","DOI":"10.1109\/JSTARS.2014.2375932","article-title":"Fast implementation of singular spectrum analysis for effective feature extraction in hyperspectral imaging","volume":"8","author":"Zabalza","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4440","DOI":"10.1364\/AO.53.004440","article-title":"Structured covaciance principle component analysis for real-time onsite feature extraction and dimensionality reduction in hyperspectral imaging","volume":"53","author":"Zabalza","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.isprsjprs.2014.04.006","article-title":"Novel Folded-PCA for Improved Feature Extraction and Data Reduction with Hyperspectral Imaging and SAR in Remote Sensing","volume":"93","author":"Zabalza","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6663","DOI":"10.1109\/TGRS.2015.2445767","article-title":"Classification of hyperspectral images by exploiting spectral-spatial information of superpixel via multiple kernels","volume":"53","author":"Fang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","article-title":"Extreme learning machine: Theory and applications","volume":"70","author":"Huang","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2483","DOI":"10.1016\/j.neucom.2010.11.030","article-title":"A study on effectiveness of extreme learning machine","volume":"74","author":"Wang","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.neucom.2008.01.005","article-title":"A fast pruned-extreme learning machine for classification problem","volume":"72","author":"Rong","year":"2008","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.neucom.2010.02.019","article-title":"Optimization method based extreme learning machine for classification","volume":"74","author":"Huang","year":"2010","journal-title":"Neurocomputing"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1109\/JSTARS.2014.2301775","article-title":"Ensemble Extreme Learning Machines for Hyperspectral Image Classification","volume":"7","author":"Samat","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/TSMCB.2011.2168604","article-title":"Extreme learning machine for regression and multiclass classification","volume":"42","author":"Huang","year":"2012","journal-title":"IEEE Trans. Syst. Man Cybern. B Cybern."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1858","DOI":"10.1109\/TCYB.2014.2298235","article-title":"Sparse extreme learning machine for classification","volume":"44","author":"Bai","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2351","DOI":"10.1109\/JSTARS.2014.2359965","article-title":"Extreme learning machine with composite kernels for hyperspectral image classification","volume":"8","author":"Zhou","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5795","DOI":"10.3390\/rs6065795","article-title":"Spectral-spatial classification of hyperspectral image based on kernel extreme learning machine","volume":"6","author":"Chen","year":"2014","journal-title":"Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Duan, W., Li, S., and Fang, L. (2014). Spectral-spatial hyperspectral image classification using superpixel and extreme learning machines. Chinese Conference on Pattern Recognition, Springer.","DOI":"10.1007\/978-3-662-45646-0_17"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1080\/01431161.2014.999882","article-title":"ELM-based spectral\u2013spatial classification of hyperspectral images using extended morphological profiles and composite feature mappings","volume":"36","author":"Heras","year":"2015","journal-title":"Int. J. Remote Sens."},{"key":"ref_24","unstructured":"Yedidia, J.S., Freeman, W.T., and Weiss, Y. (2003). Understanding belief propagation and its generalizations. Exploring Artificial Intelligence in the New Millennium, Morgan Kaufmann Publishers Inc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1109\/TIT.2005.850085","article-title":"Constructing free-energy approximations and generalized belief propagation algorithms","volume":"51","author":"Yedidia","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/JPROC.2012.2197589","article-title":"Advances in spectral-spatial classification of hyperspectral images","volume":"101","author":"Fauvel","year":"2013","journal-title":"Proc. IEEE."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1109\/LGRS.2010.2047711","article-title":"SVM-and MRF-based method for accurate classification of hyperspectral images","volume":"7","author":"Tarabalka","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1109\/TGRS.2013.2263282","article-title":"Spectral-spatial classification of hyperspectral images based on hidden Markov random fields","volume":"52","author":"Ghamisi","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1109\/JSTARS.2015.2407493","article-title":"Dynamic ensemble selection approach for hyperspectral image classification with joint spectral and spatial information","volume":"8","author":"Damodaran","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3681","DOI":"10.1109\/TGRS.2014.2381602","article-title":"Local binary patterns and extreme learning machine for hyperspectral imagery classification","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s11263-006-7007-9","article-title":"Discriminative random fields","volume":"68","author":"Kumar","year":"2006","journal-title":"Int. J. Comput. Vis."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, S.Z. (1994). Markov Random Field Modeling in Computer Vision, Springer.","DOI":"10.1007\/978-4-431-66933-3"},{"key":"ref_33","unstructured":"Borges, J.S., Mar\u00e7al, A.R.S., and Bioucas-Dias, J.M. (2003, January 23\u201328). Evaluation of Bayesian hyperspectral image segmentation with a discriminative class learning. Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing, Barcelona, Spain."},{"key":"ref_34","first-page":"4085","article-title":"Semisupervised hyperspectral image segmentation using multinomial logistic regression with active learning","volume":"4298","author":"Li","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Huang, S., Zhang, H., and Pizurica, A. (2017). A Robust Sparse Representation Model for Hyperspectral Image Classification. Sensors, 17.","DOI":"10.3390\/s17092087"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","article-title":"Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images","volume":"6","author":"Geman","year":"1984","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3947","DOI":"10.1109\/TGRS.2011.2128330","article-title":"Hyperspectral image segmentation using a new Bayesian approach with active learning","volume":"49","author":"Li","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1109\/TGRS.2014.2344442","article-title":"Supervised spectral\u2013spatial hyperspectral image classification with weighted Markov random fields","volume":"53","author":"Sun","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","unstructured":"Bioucas-Dias, J., and Figueiredo, M. (2009). Logistic Regression via Variable Splitting and Augmented Lagrangian Tools, Instituto Superior T\u00e9cnico. Technical Report."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Li, H., Li, C., Zhang, C., Liu, Z., and Liu, C. (2017). Hyperspectral Image Classification with Spatial Filtering and \u21132,1 Norm. Sensors, 17.","DOI":"10.3390\/s17020314"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1109\/TGRS.2010.2048116","article-title":"Morphological attribute profiles for the analysis of very high resolution images","volume":"48","author":"Mura","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/11\/2603\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:49:10Z","timestamp":1760208550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/11\/2603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,13]]},"references-count":41,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["s17112603"],"URL":"https:\/\/doi.org\/10.3390\/s17112603","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,13]]}}}