Kernel-based fisher discriminant analysis for hyperspectral target detection

A new method based on kernel Fisher discriminant analysis (KFDA) is proposed for target detection of hyperspectral images. The KFDA combines kernel mapping derived from support vector machine and the classical linear Fisher discriminant analysis (LFDA), and it possesses good ability to process nonlinear data such as hyperspectral images. According to the Fisher rule that the ratio of the between-class and within-class scatters is maximized, the KFDA is used to obtain a set of optimal discriminant basis vectors in high dimensional feature space. All pixels in the hyperspectral images are projected onto the discriminant basis vectors and the target detection is performed according to the projection result. The numerical experiments are performed on hyperspectral data with 126 bands collected by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The experimental results show the effectiveness of the proposed detection method and prove that this method has good ability to overcome small sample size and spectral variability in the hyperspectral target detection.