Efficient Additive Kernels via Explicit Feature Maps

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Efficient Additive Kernels via Explicit Feature Maps
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 2 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 t...
Andrea Vedaldi, Andrew Zisserman
Added 01 Apr 2010
Updated 14 May 2010
Type Conference
Year 2010
Where CVPR
Authors Andrea Vedaldi, Andrew Zisserman
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