  Hilbert-Schmidt independence criterion and distance covariance are methods to
describe independence of random variables using either the Kronecker product of
positive definite kernels or the Kronecker product of conditionally negative
definite kernels. In this paper we generalize both methods by providing an
independence criteria using a new concept, of positive definite independent
kernels. We provide a characterization of the radial kernels that are positive
definite independent on all Euclidean spaces and we present several examples.
