  We propose a novel approach for pixel classification in hyperspectral images,
leveraging on both the spatial and spectral information in the data. The
introduced method relies on a recently proposed framework for learning on
distributions -- by representing them with mean elements in reproducing kernel
Hilbert spaces (RKHS) and formulating a classification algorithm therein. In
particular, we associate each pixel to an empirical distribution of its
neighbouring pixels, a judicious representation of which in an RKHS, in
conjunction with the spectral information contained in the pixel itself, give a
new explicit set of features that can be fed into a suite of standard
classification techniques -- we opt for a well-established framework of support
vector machines (SVM). Furthermore, the computational complexity is reduced via
random Fourier features formalism. We study the consistency and the convergence
rates of the proposed method and the experiments demonstrate strong performance
on hyperspectral data with gains in comparison to the state-of-the-art results.
