Non-linear low-rank and sparse representation for hyperspectral image analysis

In this paper, we tackle the problem of unsupervised classification of hyperspectral images. We propose a clustering method based on graphs representing the data structure, which is assumed to be an union of multiple manifolds. The method constraints the pixels to be expressed as a low-rank and sparse combination of the others in a reproducing kernel Hilbert spaces (RKHS). This captures the global (low-rank) and local (sparse) structures. Spectral clustering is applied on the graph to assign the pixels to the different manifolds. A large scale approach is proposed, in which the optimization is first performed on a subset of the data and then it is applied to the whole image using a non-linear collaborative representation respecting the manifolds structure. Experiments on two hyperspectral images show very good unsupervised classification results compared to competitive approaches.