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We study the expressive power of kernel methods and the algorithmicfeasibility of multiple kernel learning for a special rich class of kernels.  Specifically, we define \emph{Euclidean kernels}, a diverse class thatincludes most, if not all, families of kernels studied in literature such aspolynomial kernels and radial basis functions. We then describe the geometricand spectral structure of this family of kernels over the hypercube (and tosome extent for any compact domain). Our structural results allow us to provemeaningful limitations on the expressive power of the class as well as deriveseveral efficient algorithms for learning kernels over different domains.

On the Expressive Power of Kernel Methods and the Efficiency of Kernel Learning by Association Schemes