Kernel-Based Domain-Invariant Feature Selection in Hyperspectral Images for Transfer Learning

This paper presents a kernel-based feature selection method for the classification of hyperspectral images. The proposed method aims at selecting a subset of the original features that are both 1) relevant (discriminant) for the considered classification problem, i.e., preserve the functional relationship between input and output variables, and 2) invariant (stable) across different domains, i.e., minimize the data-set shift between the source and the target domains. Domains can be associated with hyperspectral images collected either on different geographical areas or on the same area at different times. We propose a novel measure of data-set shift for evaluating the domain stability, which computes the distance of the conditional distributions between the source and target domains in a reproducing kernel Hilbert space. Such a measure is defined on the basis of the kernel embeddings of the conditional distributions resulting in a nonparametric approach that does not require estimating the distribution of the classes. The adopted search strategy is based on a multiobjective optimization algorithm, which optimizes the two terms of the criterion function for the estimation of the Pareto-optimal solutions. This results in an effective approach of performing feature selection in a transfer learning setting. The experimental results obtained on two hyperspectral images show the effectiveness of the proposed method in selecting features with high generalization capabilities.