Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods.
Abstract. Minimum volume covering ellipsoid estimation is important in areas such as systems identification, control, video tracking, sensor management, and novelty detection. It is well known that finding the minimum volume covering ellipsoid (MVCE) reduces to a convex optimisation problem. We propose a regularised version of the MVCE problem, and derive its dual formulation. This makes it possible to apply the MVCE problem in kernel-defined feature spaces. The solution is generally sparse, in the sense that the solution depends on a limited set of points. We argue that the MVCE is a valuable alternative to the minimum volume enclosing hypersphere for novelty detection. It is clearly a less conservative method. Besides this, we can show using statistical learning theory that the probability of a typical point being misidentified as a novelty is generally small. We illustrate our results on real data.
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