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The increase in spatial and spectral resolution of the satellite sensors, along with the shortening of the time-revisiting periods, has provided high-quality data for remote sensing image classification. However, the high-dimensional feature space induced by using many heterogeneous information sources precludes the use of simple classifiers: thus, a proper feature selection is required for discarding irrelevant features and adapting the model to the specific problem. This paper proposes to classify the images and simultaneously to learn the relevant features in such high-dimensional scenarios. The proposed method is based on the automatic optimization of a linear combination of kernels dedicated to different meaningful sets of features. Such sets can be groups of bands, contextual or textural features, or bands acquired by different sensors. The combination of kernels is optimized through gradient descent on the support vector machine objective function. Even though the combination is linear, the ranked relevance takes into account the intrinsic nonlinearity of the data through kernels. Since a naive selection of the free parameters of the multiple-kernel method is computationally demanding, we propose an efficient model selection procedure based on the kernel alignment. The result is a weight (learned from the data) for each kernel where both relevant and meaningless image features automatically emerge after training the model. Experiments carried out in multi- and hyperspectral, contextual, and multisource remote sensing data classification confirm the capability of the method in ranking the relevant features and show the computational efficience of the proposed strategy.