Automatically assigned DDC number: 00632

Manually assigned DDC number: 00631

Number of references: 4

Title: Fast Approximation of Support Vector Kernel Expansions, and an Interpretation of Clustering as Approximation in Feature Spaces

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Author:

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Subject: Bernhard Scholkopf,Phil Knirsch,Alex Smola,Chris Burges Fast Approximation of Support Vector Kernel Expansions, and an Interpretation of Clustering as Approximation in Feature Spaces

Description: . Kernel-based learning methods provide their solutions as expansions in terms of a kernel. We consider the problem of reducing the computational complexity of evaluating these expansions by approximating them using fewer terms. As a by-product, we point out a connection between clustering and approximation in reproducing kernel Hilbert spaces generated by a particular class of kernels. 1 Introduction Recent years have seen a surge in the interest in learning methods based on Mercer kernels, i.e. functions k(x; y) which for all data sets fx 1 ; : : : ; x ` g ae R N give rise to positive matrices K ij := k(x i ; x j ) [10]. Using k instead of a dot product in R N corresponds to mapping the data into a possibly high-dimensional space F by a (usually nonlinear) map Phi : R N ! F , and taking the dot product there, i.e. [2] k(x; y) = (Phi(x) Delta Phi(y)): (1) Any linear algorithm which can be carried out in terms of dot products can be made nonlinear by substituting an a prior...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1998-07-20

Pubyear: 1998

Format: ps

Identifier: http://citeseer.ist.psu.edu/147434.html

Source: http://svm.first.gmd.de/./papers/dagm.ps.gz

Language: en

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Rights: unrestricted

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