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In this letter, a method to optimally determine the kernel bandwidth of the Gaussian radial basis function (RBF) kernel for support vector (SV)-based hyperspectral anomaly detection is presented. In this method, the support of a local background distribution is first nonparametrically learned by a technique called SV data description (SVDD). The SVDD optimally models an enclosing hypersphere around the local background data in a high-dimensional feature space associated with the Gaussian RBF kernel. Any test pixel that lies outside this hypersphere surrounding the local background is considered an anomaly and, hence, a possible target pixel. Considerable improvement in detection performance due to kernel parameter optimization can be seen in the simulation results when the algorithm is applied to hyperspectral images.