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

We study the expressive power of kernel methods and the algorithmic\nfeasibility of multiple kernel learning for a special rich class of kernels.\n Specifically, we define \\emph{Euclidean kernels}, a diverse class that\nincludes most, if not all, families of kernels studied in literature such as\npolynomial kernels and radial basis functions. We then describe the geometric\nand spectral structure of this family of kernels over the hypercube (and to\nsome extent for any compact domain). Our structural results allow us to prove\nmeaningful limitations on the expressive power of the class as well as derive\nseveral efficient algorithms for learning kernels over different domains.\n