On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Tutorial on Practical Prediction Theory for Classification
The Journal of Machine Learning Research
Estimating the Support of a High-Dimensional Distribution
Neural Computation
Computation of Minimum-Volume Covering Ellipsoids
Operations Research
Local Metric Learning on Manifolds with Application to Query---Based Operations
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
The minimum volume ellipsoid metric
Proceedings of the 29th DAGM conference on Pattern recognition
Duality of Ellipsoidal Approximations via Semi-Infinite Programming
SIAM Journal on Optimization
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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.