Abstract
Due to the high dimensionality of hyperspectral image (HSI), dimension reduction or feature extraction is usually needed before the HSI classification. Traditional linear discriminant analysis (LDA) method for feature extraction usually encounters difficulty because the available training samples in HSI classification are limited, which causes the singularity of data scatter matrix. In this paper, we propose a sparse matrix transform-based LDA (SMT-LDA) algorithm for the HSI classification. By using SMT, the total scatter matrix used in LDA can be constrained to have an eigen-decomposition where the eigenvectors can be sparsely parametrized by a limited number of Givens rotations. In this way, the estimated scatter matrix is always positive definite and well conditioned even in the case of limited training samples. The proposed SMT-LDA method is compared with regularized LDA and PCA-LDA methods on two benchmark hyperspectral data sets. Experimental results indicate that the performance of the proposed method is overall superior to these methods, especially for small-sample-size classification.
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Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants Nos. 61306070 and 11371007, by the Natural Science Foundation of Hubei Province under Grant No. 2015CFB327, and by the special fund from the State Key Joint Laboratory of Environment Simulation and Pollution Control (Research Center for Eco-environmental Sciences, Chinese Academy of Sciences) (Project No. 15K02ESPCR). The authors would like to thank Prof. D. Landgrebe for providing the Indian Pines data set, Prof. C.A. Bouman for sharing SMT codes, and Prof. C. Lin for providing LIBSVM toolbox.
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Peng, J., Luo, T. Sparse matrix transform-based linear discriminant analysis for hyperspectral image classification. SIViP 10, 761–768 (2016). https://doi.org/10.1007/s11760-015-0808-y
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DOI: https://doi.org/10.1007/s11760-015-0808-y