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Hyperspectral images, which store a hundred or more spectral bands ofreflectance, have become an important data source in natural and socialsciences. Hyperspectral images are often generated in large quantities at arelatively coarse spatial resolution. As such, unsupervised machine learningalgorithms incorporating known structure in hyperspectral imagery are needed toanalyze these images automatically. This work introduces the Spatial-SpectralImage Reconstruction and Clustering with Diffusion Geometry (DSIRC) algorithmfor partitioning highly mixed hyperspectral images. DSIRC reduces measurementnoise through a shape-adaptive reconstruction procedure. In particular, foreach pixel, DSIRC locates spectrally correlated pixels within a data-adaptivespatial neighborhood and reconstructs that pixel's spectral signature usingthose of its neighbors. DSIRC then locates high-density, high-purity pixels farin diffusion distance (a data-dependent distance metric) from otherhigh-density, high-purity pixels and treats these as cluster exemplars, givingeach a unique label. Non-modal pixels are assigned the label of their diffusiondistance-nearest neighbor of higher density and purity that is already labeled.Strong numerical results indicate that incorporating spatial informationthrough image reconstruction substantially improves the performance ofpixel-wise clustering.

Unsupervised Spatial-spectral Hyperspectral Image Reconstruction and Clustering with Diffusion Geometry