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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 paper is related to the error analysis of Support Vector Machine (SVM) classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernels as the Mercer kernel and give the error estimate with De La Vallée Poussin means which improve the approximation error. On the other hand, the distortion is replaced by the uniformly boundedness of the Cesàro means. We also introduce...
This paper presents a new implementable algorithm for solving the Lipschitz classifier that is a generalization of the maximum margin concept from Hilbert to Banach spaces. In contrast to the support vector machine approach, our algorithm is free to use any finite family of continuously differentiable functions which linearly compose the decision function. Nevertheless, robustness properties are maintained...
The dynamic time warping (DTW) is state-of-the-art distance measure widely used in sequential pattern matching and it outperforms Euclidean distance in most cases because its matching is elastic and robust. It is tempting to substitute DTW distance for Euclidean distance in the Gaussian RBF kernel and plug it into the state-of-the art classifier support vector machines (SVMs) for sequence classification...
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