A Generalized Representer Theorem
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces
The Journal of Machine Learning Research
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Support Vector Machines
Hilbert Space Embeddings and Metrics on Probability Measures
The Journal of Machine Learning Research
The Journal of Machine Learning Research
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Over the last few years, two different notions of positive definite (pd) kernels---universal and characteristic---have been developing in parallel in machine learning: universal kernels are proposed in the context of achieving the Bayes risk by kernel-based classification/regression algorithms while characteristic kernels are introduced in the context of distinguishing probability measures by embedding them into a reproducing kernel Hilbert space (RKHS). However, the relation between these two notions is not well understood. The main contribution of this paper is to clarify the relation between universal and characteristic kernels by presenting a unifying study relating them to RKHS embedding of measures, in addition to clarifying their relation to other common notions of strictly pd, conditionally strictly pd and integrally strictly pd kernels. For radial kernels on ℜd, all these notions are shown to be equivalent.