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Hyperspectral imaging fully portrays materials through numerous and contiguous spectral bands. It is a very useful technique in various fields, including astronomy, medicine, food safety, forensics, and target detection. However, hyperspectral images include redundant measurements, and most classification studies encountered the Hughes phenomenon. Finding a small subset of effective features to model the characteristics of classes represented in the data for classification is a critical preprocessing step required to render a classifier effective in hyperspectral image classification. In our previous work, an automatic method for selecting the radial basis function (RBF) parameter (i.e., σ) for a support vector machine (SVM) was proposed. A criterion that contains the between-class and within-class information was proposed to measure the separability of the feature space with respect to the RBF kernel. Thereafter, the optimal RBF kernel parameter was obtained by optimizing the criterion. This study proposes a kernel-based feature selection method with a criterion that is an integration of the previous work and the linear combination of features. In this new method, two properties can be achieved according to the magnitudes of the coefficients being calculated: the small subset of features and the ranking of features. Experimental results on both one simulated dataset and two hyperspectral images (the Indian Pine Site dataset and the Pavia University dataset) show that the proposed method improves the classification performance of the SVM.