The Gaussian radial basis function (RBF) is a widely used kernel in kernel-based methods. parameter RBF, referred to as the shape parameter, plays an essential role model fitting. In this paper, we propose method select parameters for general RBF kernel. It can simultaneously serve variable selection and regression estimation. For former, asymptotic consistency established; latter, estimation e...

Kernel Principal Component Analysis (KPCA) has proven to be a versatile tool for unsupervised learning, however at a high computational cost due to the dense expansions in terms of kernel functions. We overcome this problem by proposing a new class of feature extractors employing`1 norms in coeecient space instead of the reproducing kernel Hilbert space in which KPCA was originally formulated i...

In this paper, we study deep signal representations that are invariant to groups of transformations and stable to the action of diffeomorphisms without losing signal information. This is achieved by generalizing the multilayer kernel construction introduced in the context of convolutional kernel networks and by studying the geometry of the corresponding reproducing kernel Hilbert space. We show...

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. further present general setting using bilinear forms, we provide examples. Our results cover case measurable kernels, applications both stochastic analysis metric geometry number