This paper introduces a nonlinear measure of dependence between random
variables in the context of remote sensing data analysis. The Hilbert-Schmidt
Independence Criterion (HSIC) is a kernel method for evaluating statistical
dependence. HSIC is based on computing the Hilbert-Schmidt norm of
the cross-covariance operator of mapped samples in the corresponding
Hilbert spaces. The HSIC empirical estimator is very easy to compute
and has good theoretical and practical properties. We exploit the
capabilities of HSIC to explain nonlinear dependences in two remote
sensing problems: temperature estimation and chlorophyll concentration
prediction from spectra. Results show that, when the relationship
between random variables is nonlinear or when few data are available,
the HSIC criterion outperforms other standard methods, such as the
linear correlation or mutual information.