title: Hyperellipsoidal statistical classifications in a reproducing kernel Hilbert space.
abstract: Standard support vector machines (SVMs) have kernels based on the Euclidean distance. This brief extends standard SVMs to SVMs with kernels based on the Mahalanobis distance. The extended SVMs become a special case of the Euclidean distance when the covariance matrix in a reproducing kernel Hilbert space is degenerated to an identity. The Mahalanobis distance leads to hyperellipsoidal kernels and the Euclidean distance results in hyperspherical ones. In this brief, the Mahalanobis distance-based kernel in a reproducing kernel Hilbert space is developed systematically. Extensive experiments demonstrate that the hyperellipsoidal kernels slightly outperform the hyperspherical ones, with fewer SVs.
authors.affiliation: School of Information, Remin University of China, Beijing, China. xliang@ruc.edu.cn
authors.forename: Xun
authors.initials: X
authors.lastname: Liang
authors.forename: Zhihao
authors.initials: Z
authors.lastname: Ni
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*