Spatial–spectral locality constrained elastic net hypergraph for hyperspectral image clustering

Hypergraph is an effective method used to represent the contextual correlation within hyperspectral imagery for clustering. Nevertheless, how to discover the closely correlated samples to form hyperedges is the key issue for constructing an informative hypergraph. In this article, a new spatial–spectral locality constrained elastic net hypergraph learning model is proposed for hyperspectral image clustering i.e. unsupervised classification. In order to utilize the spatial–spectral correlation among the pixels in hyperspectral images, first, we construct a locality-constrained dictionary by selecting K relevant pixels within a spatial neighbourhood, which activates the most correlated atoms and suppresses the uncorrelated ones. Second, each pixel is represented as a linear combination of the atoms in the dictionary under the elastic net regularization. Third, based on the obtained representations, the pixels and their most related pixels are linked as hyperedges, which can effectively capture high–order relationships among the pixels. Finally, a hypergraph Laplacian matrix is built for unsupervised learning. Experiments have been conducted on two widely used hyperspectral images, and the results show that the proposed method can achieve a superior clustering performance when compared to state-of-the-art methods.