Spectral-Spatial Diffusion Geometry for Hyperspectral Image Clustering

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data that leverages spatially regularized random walks is proposed. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone. The regularized diffusion process is subsequently used to embed the high-dimensional HSI into a lower-dimensional space through diffusion distances. Cluster modes are computed using kernel density estimation and diffusion distances, and all other points are labeled according to these modes. The proposed method has low computational complexity and performs competitively against state-of-the-art HSI clustering algorithms on real data. In particular, the proposed spatial regularization confers both theoretical and empirical advantages over nonregularized methods.