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The technological evolution of optical sensors over the last few decades has provided remote sensing analysts with rich spatial, spectral, and temporal information. In particular, the increase in spectral resolution of hyperspectral images (HSIs) and infrared sounders opens the doors to new application domains and poses new methodological challenges in data analysis. HSIs allow the characterization of objects of interest (e.g., land-cover classes) with unprecedented accuracy, and keeps inventories up to date. Improvements in spectral resolution have called for advances in signal processing and exploitation algorithms. This article focuses on the challenging problem of hyperspectral image classification, which has recently gained in popularity and attracted the interest of other scientific disciplines such as machine learning, image processing, and computer vision. In the remote sensing community, the term classification is used to denote the process that assigns single pixels to a set of classes, while the term segmentation is used for methods aggregating pixels into objects and then assigned to a class.