measuring Statistical Dependence with Hilbert-Schmidt Norm

An independence criterion based on covariance operators in reproducing kernel Hilbert spaces (RKHSs) is proposed. Also an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator, referred to as Hilbert-Schmidt Independence Criterion, or HSIC is given. This can be used as dependence measure in practical application such as independent Component Analysis (ICA), Maximum Variance Unfolding (MVU), feature extraction, feature selection, ... .