Optimal kernel bandwidth estimation for hyperspectral kernel-based anomaly detection

A kernel-based anomaly detection technique called Kernel RX algorithm has been developed earlier by one of the authors, to be used as a prescreening tool that non-linearly detects anomalous pixel spectra in hyperspectral images. Targets of interest are then identified among the prescreened anomalous spectra based on reference spectral information using supervised classification/detection techniques. Kernel RX algorithm uses kernels like the Gaussian radial basis function (RBF) kernel to transform the given data into higher-dimensional (possibly infinite) feature space before detecting the anomalies. The efficiency of the algorithm depends on this transformation which in turn depends on the respective kernel parameters. The Gaussian RBF kernel has a parameter called bandwidth parameter. In this paper, a new method to determine the optimal full diagonal bandwidth parameters of the Gaussian RBF kernel is presented. First, cross-validation technique is used to estimate an optimal single bandwidth parameter. Then, the full diagonal parameters are estimated from this single parameter using the variances of the spectral bands of the hyperspectral image. It will be shown that the optimal full diagonal bandwidth parameters provide a better probability of detection at a given false alarm rate compared to the optimal single bandwidth parameter and other suboptimal bandwidth parameters when tested on hyperspectral imagery for military target detection.