  Hyperspectral images, which store a hundred or more spectral bands of
reflectance, have become an important data source in natural and social
sciences. Hyperspectral images are often generated in large quantities at a
relatively coarse spatial resolution. As such, unsupervised machine learning
algorithms incorporating known structure in hyperspectral imagery are needed to
analyze these images automatically. This work introduces the Spatial-Spectral
Image Reconstruction and Clustering with Diffusion Geometry (DSIRC) algorithm
for partitioning highly mixed hyperspectral images. DSIRC reduces measurement
noise through a shape-adaptive reconstruction procedure. In particular, for
each pixel, DSIRC locates spectrally correlated pixels within a data-adaptive
spatial neighborhood and reconstructs that pixel's spectral signature using
those of its neighbors. DSIRC then locates high-density, high-purity pixels far
in diffusion distance (a data-dependent distance metric) from other
high-density, high-purity pixels and treats these as cluster exemplars, giving
each a unique label. Non-modal pixels are assigned the label of their diffusion
distance-nearest neighbor of higher density and purity that is already labeled.
Strong numerical results indicate that incorporating spatial information
through image reconstruction substantially improves the performance of
pixel-wise clustering.
