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Efficient Additive Kernels via Explicit Feature Maps
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@MISC{Vedaldi_efficientadditive,
author = {Andrea Vedaldi and Andrew Zisserman},
title = {Efficient Additive Kernels via Explicit Feature Maps},
year = {}
}
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Abstract
Maji and Berg [13] have recently introduced an explicit feature map approximating the intersection kernel. This enables efficient learning methods for linear kernels to be applied to the non-linear intersection kernel, expanding the applicability of this model to much larger problems. In this paper we generalize this idea, and analyse a large family of additive kernels, called homogeneous, in a unified framework. The family includes the intersection, Hellinger’s, and χ2 kernels commonly employed in computer vision. Using the framework we are able to: (i) provide explicit feature maps for all homogeneous additive kernels along with closed form expression for all common kernels; (ii) derive corresponding approximate finitedimensional feature maps based on the Fourier sampling theorem; and (iii) quantify the extent of the approximation. We demonstrate that the approximations have indistinguishable performance from the full kernel on a number of standard datasets, yet greatly reduce the train/test times of SVM implementations. We show that the χ2 kernel, which has been found to yield the best performance in most applications, also has the most compact feature representation. Given these train/test advantages we are able to obtain a significant performance improvement over current state of the art results based on the intersection kernel. 1.
Keyphrases
explicit feature map efficient additive kernel intersection kernel compact feature representation indistinguishable performance closed form expression common kernel additive kernel train test time homogeneous additive kernel computer vision svm implementation full kernel standard datasets approximate finitedimensional feature map non-linear intersection kernel large family linear kernel art result current state unified framework significant performance improvement
