Mahalanobis Ellipsoidal Learning Machine for One Class Classification

In this paper, we propose a novel kernel Mahalanobis ellipsoidal learning machine for one class classification. We propose to incorporate with the sample covariance matrix information and thus utilize the Mahalanobis distance rather than Euclidean distance in standard support vector data description. We use the centered kernel matrix and the singular value decomposition method to estimate the inverse of the sample covariance matrix. To avoid the existence of zero eigenvalues of the sample covariance matrix in high-dimensional feature space, we also introduce an uncertainty model to address a robust optimization problem. We investigate the initial performances of Mahalanobis ellipsoidal learning machine using the UCI benchmark datasets.