Mahalanobis kernel based on probabilistic principal component

A kernel adapted to the spectral dimension of hyperspectral images is proposed in this paper. A distance based on a statistical cluster model is used to construct a radial kernel. This class specific kernel realizes a compromise between a conventional Gaussian kernel and a Gaussian kernel on the first principal components of the considered class. An automatic gradient optimization is used to select the optimal hyperparameters. Experimental results on a real hyperspectral image show the kernel is effective compared to the conventional Gaussian kernel. Furthermoren the proposed kernel is less sensitive to one hyperparameter compared to the Gaussian kernel applied on the first principal components of the data.