Abstract--In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. In [12] a novel RBF network with the multi-kernel is proposed to obtain an optimized and I. INTRODUCTION The unknown centres of the multikernels The RBF neural networks have shown excellent performance are determined by an improved k-means clustering in a number of problems of practical interest. An orthogonal least squares (OLS) algorithm is reservoirs of brine are analyzed for physicochemical properties used to determine the remaining parameters. The convergence of the ACA is analyzed by the [3] the RBF kernel is used to predict the pressure gradient Lyapunov criterion. In the context of nuclear physics, RBF Cognitive Radial Basis Function network (McRBFN) and its has been effectively used to model the stopping power data Projection based Learning (PBL) referred to as PBL-McRBFN of materials as in [4].

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.