Abstract
Support vector machine (SVM) is a powerful cognitive and learning algorithm in the domain of pattern recognition and image classification. However, the generalization ability of SVM is limited when processing classification of high-resolution remote sensing images. One chief reason for this is that the Euclidean distance-based distance matrix in traditional SVM treats different samples equally and overlooks the global distribution of samples. To construct a more effective SVM-based classification method, this paper proposes a multi-scale Mahalanobis kernel-based SVM classifier. In this new method, we first introduce a Mahalanobis distance kernel to improve the global cognitive learning ability of SVM. Then, the Mahalanobis distance kernel is embedded to the multi-scale kernel learning (MSKL) to construct a novel multi-scale Mahalanobis kernel, in which the parameters are optimized by a bio-inspired algorithm, named differential evolution. Finally, the new method is extended to the classification of high-resolution remote sensing images based on the spatial-spectral features. The comparison experiments of five public UCI datasets and two high-resolution remote sensing images verify that the Mahalanobis distance-based method can obtain more accurate classification results than that of the Euclidean distance-based method. In addition, the proposed method produced the best classification results in all the experiments. The global cognitive learning ability of Mahalanobis distance-based method is stronger than that of the Euclidean distance-based method. In addition, this study indicates that the optimized MSKL are potential for the interpretation and understanding of complicated high-resolution remote sensing scene.
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References
Aljarah I, Al-Zoubi AM, Faris H, et al. Simultaneous feature selection and support vector machine optimization using the grasshopper optimization algorithm. Cogn Comput. 2018;10(3):478–95.
Vapnik V. An overview of statistical learning theory. IEEE Trans Neural Netw. 1999;10(5):988–99.
Schölkopf B, Smola A. Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press; 2001.
Anbar M, Abdullah R, Al-Tamimi BN, et al. A machine learning approach to detect router advertisement flooding attacks in next-generation IPV6 networks. Cogn Comput. 2018;10(2):201–14.
Pang J, Zhao Y-H, Xu J, et al. Super-graph classification based on composite subgraph features and extreme learning machine. Cogn Comput. 2018;10(6):922–36.
Li P, Sun M, Wang Z, Chai B. OPTICS-based unsupervised method for flaking degree evaluation on the murals in Mogao Grottoes. Sci Rep. 2018;8(1):15954.
Sun M, Zhang D, Wang Z, Ren J, Chai B, Sun J. What’s wrong with the murals at the Mogao Grottoes: a near-infrared hyperspectral imaging method. Sci Rep. 2015;5:14371.
Vladimir V, Olivier C, Olivier B. Choosing multiple parameters for support vector machines. Mach Learn. 2002;46(1–3):131–59.
Tanveer M. Robust and sparse linear programming twin support vector machines. Cogn Comput. 2015;7(1):137–49.
Phienthrakul T, Kijsirikul B. Evolutionary strategies for multi-scale radial basis function kernels in support vector machines. In: Proceedings of the Conf. Genet. Evol. Comput. Washington D. C., USA: ACM; 2005. p. 905–11.
Ong C-S, Smola A-J, Williamson R-C. Learning the kernel with hyperkernels. J Mach Learn Res. 2005;6:1043–71.
Damoulas T, Girolami MA. Probabilistic multi-class multi-kernel learning: on protein fold recognition and remote homology detection. Bioinformatics. 2008;24(10):1264–70.
Li H-C, Chu H, Huo Y-H. Multi-feature multiple kernels SVM-based urban road extraction. Bull Surv Mapp. 2018;2:72–7.
Lanckriet GRG, Cristianini N, Bartlett P, et al. Learning the kernel matrix with semidefinite programming. J Mach Learn Res. 2004;5(1):27–−72.
Bao J, Chen Y-Y, Yu L, et al. A multi-scale kernel learning method and its application in image classification. Neurocomputing. 2017;257:16–23.
Lu Y-W, Lai Z-H, Li X-L, et al. Learning parts-based and global representation for image classification. IEEE Trans Circuits Syst Video Technol. 2018;28(12):3345–60.
Gao F, Mei J, Sun J, Wang J, Yang E, Hussain A. A novel classification algorithm based on incremental semi-supervised support vector machine. PLoS One. 2015;10(8):e0135709.
Gao F, Lv W, Zhang Y, Sun J, Wang J, Yang E. A novel semisupervised support vector machine classifier based on active learning and context information. Multidim Syst Sign Process. 2016;27(4):969–88.
Gao F, Huang T, Wang J, Sun J, Hussain A, Yang E. Dual-branch deep convolution neural network for polarimetric SAR image classification. Appl Sci. 2017;7(5):447.
Sun G, Hao Y, Rong J, et al. Combined deep learning and multiscale segmentation for rapid high resolution damage mapping. In: Proceedings of the 2017 IEEE Int. Conf. Smart Data (SmartData). Exeter, UK: IEEE; 2017. p. 1101–5.
Huang H, Sun G, Zhang X, et al. Combined multiscale segmentation convolutional neural network for rapid damage mapping from postearthquake very high-resolution images. J Appl Remote Sens. 2019;13(2):022007.
Ke T, Lv H, Sun M-J, et al. A biased least squares support vector machine based on Mahalanobis distance for PU learning. Physica A. 2018;509:422–38.
Wang Z, Ren J, Zhang D, Sun M, Jiang J. A deep-learning based feature hybrid framework for spatiotemporal saliency detection inside videos. Neurocomputing. 2018;287:68–83.
Luo Y-R. Image retrieval algorithm by integrating features fusion and support vector machine feedback. Comput Appl So. 2014;10:209–12.
Li R-B, Li A-H, Wang T. Mahalanobis distance method for unclassifiable region of support vector machine. Inform.Control. 2010;3:367–72.
Wang H, Gao Y, Zhang C. Multi-class support vector machines based on the mahalanobis distance. In: 2011 International Conference on Machine Learning and Cybernetics; 2011. p. 757–62.
Diao Z-H, Wu Y-Y. A new SVM decision tree multi-class classification algorithm based on Mahalanobis distance. In: Proceedings of the 30th Chinese Control Conference. Yantai, China:IEEE; 2011. p. 3124–7.
Xiang S-M, Nie F-P, Zhang C-S. Learning a Mahalanobis distance metric for data clustering and classification. Pattern Recogn. 2008;41(12):3600–12.
Weinberger KQ, Saul LK. Distance metric learning for large margin nearest neighbor classification. J Mach Learn Res. 2009;10:207–44.
Mensink T, Verbeek J, Perronnin F, et al. Metric learning for large scale image classification: generalizing to new classes at near-zero cost. In: Proceedings of the 12th European Conf. Computer Vision. Florence, Italy: IEEE; 2012. p. 488–−501.
Zou X-L, Liu X-Z. Sample reduction based on kernel squared Mahalanobis distance for support vector machines. Int Conf Comput Appl Syst Mod IEEE. 2010;11:272–6.
Zhang X-K, Ding S-F. Mahalanobis distance-based twin multi-class classification support vector machine. Comput Sc. 2013;5(4):580–8.
Li Y-R, Xiang G-B. A linear discriminant analysis classification algorithm based on mahalanobis distance. Comput Simul. 2006;8:86–8.
Wang X-L, Li J-C. A fast algorithm for extracting the support vector on the Mahalanobis distance. J Xidian Univ (Nat Sci). 2004;4:639–43.
Sonnenburg S, Rätsch G, Schäfer C, et al. Large scale multiple kernel learning. J Mach Learn Res. 2006;7:1531–65.
Subrahmanya N, Shin YC. Sparse multiple kernel learning for signal processing applications. IEEE Trans Pattern Anal Mach Intell. 2010;32(5):788–98.
Gu Y-F. Representative multiple kernel learning for classification in hyperspectral imagery. IEEE Trans Geosci Remote Sens. 2012;50(7):2852–65.
Kloft M. Efficient and accurate lp-norm multiple kernel learning. Adv NIPS. 2009;22(22):997–1005.
Long B, Tian S-L, Wang H-J. Feature vector selection method using Mahalanobis distance for diagnostics of analog circuits based on LS-SVM. J Electron Test-Theory Appl. 2012;28(5):745–55.
Li C, Huang J, Li Z, et al. Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method. Geophysics. 2017;83(1):S33–46.
Huang J, Liao W, Li Z. A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface. Eng Comput. 2018;35(1):334–62.
Yong P, Huang J, Li Z, et al. Optimized equivalent staggered-grid FD method for elastic wave modelling based on plane wave solutions. Geophys Suppl Mon Not Roy Astr Soc. 2016;208(2):1157–72.
Rahnamayan S, Tizhoosh HR, Salama MMA. Opposition-based differential evolution. IEEE T Evolut Comput. 2008;12(1):64–79.
Storn R, Price K. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim. 1997;11(4):341–59.
Kuffer M, Pfeffer K, Sliuzas R, et al. Extraction of slum areas from VHR imagery using GLCM variance. IEEE J-STARS. 2016;9(5):1830–40.
Wang C, Ren J, Wang H, et al. Spectral-spatial classification of hyperspectral data using spectral-domain local binary patterns. Multimed Tools Appl. 2018:1–15.
Funding
This study was funded by the National Natural Science Foundation of China (no. 41801275), the Shandong Provincial Natural Science Foundation, China (no. ZR2018BD007), and the Fundamental Research Funds for the Central Universities (nos. 18CX05030A, 18CX02179A).
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Sun, G., Rong, X., Zhang, A. et al. Multi-Scale Mahalanobis Kernel-Based Support Vector Machine for Classification of High-Resolution Remote Sensing Images. Cogn Comput 13, 787–794 (2021). https://doi.org/10.1007/s12559-019-09631-5
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DOI: https://doi.org/10.1007/s12559-019-09631-5