{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:13:36Z","timestamp":1760148816967,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62176140","62077038","61672405","2021JM-459"],"award-info":[{"award-number":["62176140","62077038","61672405","2021JM-459"]}]},{"name":"Natural Science Foundation of Shaanxi Province of China","award":["62176140","62077038","61672405","2021JM-459"],"award-info":[{"award-number":["62176140","62077038","61672405","2021JM-459"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>To extract effective features for the terrain classification of hyperspectral remote-sensing images (HRSIs), a spectral fractional-differentiation (SFD) feature of HRSIs is presented, and a criterion for selecting the fractional-differentiation order is also proposed based on maximizing data separability. The minimum distance (MD) classifier, support vector machine (SVM) classifier, K-nearest neighbor (K-NN) classifier, and logistic regression (LR) classifier are used to verify the effectiveness of the proposed SFD feature, respectively. The obtained SFD feature is sent to the full connected network (FCN) and 1-dimensionality convolutional neural network (1DCNN) for deep-feature extraction and classification, and the SFD-Spa feature cube containing spatial information is sent to the 3-dimensionality convolutional neural network (3DCNN) for deep-feature extraction and classification. The SFD-Spa feature after performing the principal component analysis (PCA) on spectral pixels is directly connected with the first principal component of the original data and sent to 3DCNNPCA and hybrid spectral net (HybridSN) models to extract deep features. Experiments on four real HRSIs using four traditional classifiers and five network models have shown that the extracted SFD feature can effectively improve the accuracy of terrain classification, and sending SFD feature to deep-learning environments can further improve the accuracy of terrain classification for HRSIs, especially in the case of small-size training samples.<\/jats:p>","DOI":"10.3390\/rs15112879","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T01:33:54Z","timestamp":1685669634000},"page":"2879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hyperspectral Remote Sensing Images Feature Extraction Based on Spectral Fractional Differentiation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3960-6902","authenticated-orcid":false,"given":"Jing","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4155-2859","authenticated-orcid":false,"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2410-435X","authenticated-orcid":false,"given":"Feng","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Shandong Technology and Business University, Yantai 264005, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9993-0731","authenticated-orcid":false,"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alcolea, A., Paoletti, M.E., Haut, J.M., Resano, J., and Plaza, A. (2020). Inference in Supervised Spectral Classifiers for On-Board Hyperspectral Imaging: An Overview. Remote Sens., 12.","DOI":"10.3390\/rs12030534"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ma, W., Yang, Q., Wu, Y., Zhao, W., and Zhang, X. (2019). Double-Branch Multi-Attention Mechanism Network for Hyperspectral Image Classification. Remote Sens., 11.","DOI":"10.3390\/rs11111307"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6690","DOI":"10.1109\/TGRS.2019.2907932","article-title":"Deep Learning for Hyperspectral Image Classification: An Overview","volume":"57","author":"Li","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/LGRS.2008.915736","article-title":"Denoising and Dimensionality Reduction Using Multilinear Tools for Hyperspectral Images","volume":"5","author":"Renard","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Li, N., Zhou, D., Shi, J., Wu, T., and Gong, M. (2021). Spectral-Locational-Spatial Manifold Learning for Hyperspectral Images Dimensionality Reduction. Remote Sens., 13.","DOI":"10.3390\/rs13142752"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1109\/LGRS.2011.2172185","article-title":"Linear Versus Nonlinear PCA for the Classification of Hyperspectral Data Based on the Extended Morphological Profiles","volume":"9","author":"Licciardi","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1109\/JSTARS.2013.2237758","article-title":"Spectral Derivative Features for Classification of Hyperspectral Remote Sensing Images: Experimental Evaluation","volume":"6","author":"Bao","year":"2013","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ye, Z., He, M., Fowler, J.E., and Du, Q. (2014, January 4). Hyperspectral Image Classification Based on Spectra Derivative Features and Locality Preserving Analysis. Proceedings of the 2014 IEEE China Summit and International Conference on Signal and Information Processing, Xi\u2019an, China.","DOI":"10.1109\/ChinaSIP.2014.6889218"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Tian, A., Zhao, J., Tang, B., Zhu, D., Fu, C., and Xiong, H. (2021). Hyperspectral Prediction of Soil Total Salt Content by Different Disturbance Degree under a Fractional-Order Differential Model with Differing Spectral Transformations. Remote Sens., 13.","DOI":"10.3390\/rs13214283"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106031","DOI":"10.1016\/j.compag.2021.106031","article-title":"Predicting the Contents of Soil Salt and Major Water-soluble Ions with Fractional-order Derivative Spectral Indices and Variable Selection","volume":"182","author":"Lao","year":"2021","journal-title":"Comput. Electron. Agric."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"114228","DOI":"10.1016\/j.geoderma.2020.114228","article-title":"Exploring the Potential of Airborne Hyperspectral Image for Estimating Topsoil Organic Carbon: Effects of Fractional-order Derivative and Optimal Band Combination Algorithm","volume":"365","author":"Hong","year":"2020","journal-title":"Geoderma"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gao, Q., Lim, S., and Jia, X. (2018). Hyperspectral Image Classification Using Convolutional Neural Networks and Multiple Feature Learning. Remote Sens., 10.","DOI":"10.3390\/rs10020299"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"258619","DOI":"10.1155\/2015\/258619","article-title":"Deep Convolutional Neural Networks for Hyperspectral Image Classification","volume":"2015","author":"Hu","year":"2015","journal-title":"J. Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.isprsjprs.2018.05.014","article-title":"Hyperspectral Image Classification Via a Random Patches Network","volume":"142","author":"Xu","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1109\/MGRS.2019.2912563","article-title":"Deep Learning for Classification of Hyperspectral Data: A Comparative Review","volume":"7","author":"Audebert","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1109\/LGRS.2019.2918719","article-title":"HybridSN: Exploring 3-D\u20132-D CNN Feature Hierarchy for Hyperspectral Image Classification","volume":"17","author":"Roy","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, W., Jia, Z., Yang, J., and Kasabov, N.K. (2022). Multispectral Image Enhancement Based on the Dark Channel Prior and Bilateral Fractional Differential Model. Remote Sens., 14.","DOI":"10.3390\/rs14010233"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4101","DOI":"10.1109\/JSTARS.2021.3068864","article-title":"A Pixel Cluster CNN and Spectral-Spatial Fusion Algorithm for Hyperspectral Image Classification with Small-Size Training Samples","volume":"14","author":"Dong","year":"2021","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1109\/LGRS.2017.2665679","article-title":"Semisupervised Hyperspectral Image Classification Using Small Sample Sizes","volume":"14","author":"Aydemir","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1515\/fca-2019-0003","article-title":"A Review on Variable-order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications","volume":"22","author":"Sun","year":"2019","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_25","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Pu, Y. (2006, January 16). Fractional Calculus Approach to Texture of Digital Image. Proceedings of the 8th International Conference on Signal Processing, Guilin, China.","DOI":"10.1109\/ICOSP.2006.345713"},{"key":"ref_27","first-page":"118","article-title":"Five Numerical Algorithms of Fractional Calculus Applied in Modern Signal Analyzing and Processing","volume":"37","author":"Pu","year":"2005","journal-title":"J. Sichuan Univ. Eng. Sci. Ed."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Vali, A., Comai, S., and Matteucci, M. (2020). Deep Learning for Land Use and Land Cover Classification Based on Hyperspectral and Multispectral Earth Observation Data: A Review. Remote Sens., 12.","DOI":"10.3390\/rs12152495"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Liu, J., Yang, Z., Liu, Y., and Mu, C. (2021). Hyperspectral Remote Sensing Images Deep Feature Extraction Based on Mixed Feature and Convolutional Neural Networks. Remote Sens., 13.","DOI":"10.3390\/rs13132599"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/11\/2879\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:47:04Z","timestamp":1760125624000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/11\/2879"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,1]]},"references-count":30,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["rs15112879"],"URL":"https:\/\/doi.org\/10.3390\/rs15112879","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,6,1]]}}}