A parameter-free kernel design based on cumulative distribution function for correntropy

This paper proposes a parameter-free kernel that is translation invariant and positive definite. The new kernel is based on the data cumulative distribution function (CDF) that provides all the statistical information about the observed samples. Without an explicit kernel size parameter, this novel kernel is used to define the autocorrentropy function, which is a generalized similarity measure, and spectral density estimator. Numerical examples show that the proposed method provides comparable performance to the existing Gaussian kernel with optimized kernel size.