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On the Expressive Power of Kernel Methods and the Efficiency of Kernel Learning by Association Schemes
We study the expressive power of kernel methods and the algorithmic
feasibility of multiple kernel learning for a special rich class of kernels.
Specifically, we define \emph{Euclidean kernels}, a diverse class that
includes most, if not all, families of kernels studied in literature such as
polynomial kernels and radial basis functions. We then describe the geometric
and spectral structure of this family of kernels over the hypercube (and to
some extent for any compact domain). Our structural results allow us to prove
meaningful limitations on the expressive power of the class as well as derive
several efficient algorithms for learning kernels over different domains