Remote Sensing Feature Selection by Kernel Dependence Measures

Gustavo Camps-Valls, Joris M. Mooij, Bernhard Schölkopf

Abstract: This letter introduces a nonlinear measure of independence between random variables for remote sensing supervised feature selection. The so-called Hilbert–Schmidt independence criterion (HSIC) is a kernel method for evaluating statistical dependence and it 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 easy to compute and has good theoretical and practical properties. Rather than using this estimate for maximizing the dependence between the selected features and the class labels, we propose the more sensitive criterion of minimizing the associated HSIC <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$p$</tex></formula> -value. Results in multispectral, hyperspectral, and SAR data feature selection for classification show the good performance of the proposed approach.