Sparse matrix transform-based linear discriminant analysis for hyperspectral image classification

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.