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# Ellipsoidal Machines

*Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics*, PMLR 2:484-491, 2007.

#### Abstract

A novel technique is proposed for improving the standard Vapnik-Chervonenkis (VC) dimension estimate for the Support Vector Machine (SVM) framework. The improved VC estimates are based on geometric arguments. By considering bounding ellipsoids instead of the usual bounding hyperspheres and assuming gap-tolerant classifiers, a linear classifier with a given margin is shown to shatter fewer points than previously estimated. This improved VC estimation method directly motivates a different estimator for the parameters of a linear classifier. Surprisingly, only VC-based arguments are needed to justify this modification to the SVM. The resulting technique is implemented using Semidefinite Programming (SDP) and is solvable in polynomial time. The new linear classifier also ensures certain invariances to affine transformations on the data which a standard SVM does not provide. We demonstrate that the technique can be kernelized via extensions to Hilbert spaces. Promising experimental results are shown on several standardized datasets.