Mahalanobis kernel for the classification of hyperspectral images

The definition of the Mahalanobis kernel for the classification of hyperspectral remote sensing images is addressed. Class specific covariance matrices are regularized by a probabilistic model which is based on the data living in a subspace spanned by the p first principal components. The inverse of the covari-ance matrix is computed in a closed form and is used in the kernel to compute the distance between two spectra. Each principal direction is normalized by a hyperparameter tuned, according to an upper error bound, during the training of an SVM classifier. Results on real data sets empirically demon-strate that the proposed kernel leads to an increase of the classification accuracy by comparison to standard kernels. Index Terms — Mahalanobis kernel, probabilistic prin-cipal component analysis, support vector machine, hyper-spectral images, classification. 1