Kernel ellipsoidal trimming

Ellipsoid estimation is important in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and statistical outlier or novelty detection. A new method, called Kernel Minimum Volume Covering Ellipsoid (KMVCE) estimation, that finds an ellipsoid in a kernel-defined feature space is presented. Although the method is very general and can be applied to many of the aforementioned problems, the main focus is on the problem of statistical novelty/outlier detection. A simple iterative algorithm based on Mahalanobis-type distances in the kernel-defined feature space is proposed for practical implementation. The probability that a non-outlier is misidentified by our algorithms is analysed using bounds based on Rademacher complexity. The KMVCE method performs very well on a set of real-life and simulated datasets, when compared with standard kernel-based novelty detection methods.