  We introduce a divergence measure between data distributions based on
operators in reproducing kernel Hilbert spaces defined by kernels. The
empirical estimator of the divergence is computed using the eigenvalues of
positive definite Gram matrices that are obtained by evaluating the kernel over
pairs of data points. The new measure shares similar properties to
Jensen-Shannon divergence. Convergence of the proposed estimators follows from
concentration results based on the difference between the ordered spectrum of
the Gram matrices and the integral operators associated with the population
quantities. The proposed measure of divergence avoids the estimation of the
probability distribution underlying the data. Numerical experiments involving
comparing distributions and applications to sampling unbalanced data for
classification show that the proposed divergence can achieve state of the art
results.
