Apply an automatic parameter selection method to generalized discriminant analysis with RBF kernel for hyperspectral image classification

Hyperspectral imaging portrays materials through numerous and contiguous spectral bands. It is an application in various fields, including astronomy, medicine, food safety, forensics, and target detection. However, hyperspectral images include redundant measurements, and most classification studies in the hyperspectral image literature encountered the Hughes phenomenon. Generalized discriminant analysis (GDA), a kernel-based (nonlinear) linear discriminant analysis (LDA), has been applied to hyperspectral image classification for avoiding the Hughes phenomenon. Nevertheless, the performances of GDA are based on choosing the proper kernel function or proper parameters of a kernel function. In our previous work, an automatic method for selecting the radial basis function (RBF) parameter, APR, for a support vector machine (SVM) was proposed. This study applies APR to determine the parameter of GDA with RBF kernel and proposes a kernel-based classification scheme for hyperspectral image classification. Experimental result on the Indian Pine Site data set shows that the proposed method can obtain accurate classification performance than k-fold cross-validation. Moreover, the time cost of the proposed method is much less than the k-fold cross-validation.