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Kernel generalized Gaussian and robust statistical learning for abnormality detection in medical images

Typical methods for abnormality detection in medical images, which is a one-class classification problem, rely on kernel principal component analysis (KPCA) and its robust invariants. However, typical methods for robust KPCA appear heuristical in nature and often ignore the variances of the data along the principal modes of variation. In this paper, we propose a novel method for robust statistical learning in a reproducing kernel Hilbert space (RKHS) that relies on our extension of the multivariate generalized Gaussian distribution to RKHS. We propose novel algorithms to fit our kernel generalized Gaussian (KGG) in RKHS, using solely the Gram matrix and without the explicit lifting map. We exploit the KGG model, including mean, principal directions, and variances, for abnormality detection in medical images. The results on two large publicly available retinopathy datasets show that our method outperforms the state of the art.