Unmixing multiple intimate mixtures via a locally low-rank representation

Hyperspectral images often contain multiple intimate (nonlinear) mixtures. When attempting to unmix such datasets it is important to identify (cluster) the different mixtures present in the data and also minimize the effects of the nonlinearities in the data due to intimate mixing (embedding). Manifold clustering and embedding techniques appear to be an ideal tool for this task. Previous work in the field of manifold clustering either make simplifying assumptions or trade-off the embedding objective to improve the clustering. This is unacceptable in the case of unmixing as the embedded data is used for future processing (for e.g. abundance estimation). We discuss a low rank neighborhood representation which expresses each point as an affine combination of its neighbors on the same manifold. This ensures that the reconstruction matrix has a block diagonal structure, enabling the identification of classes by spectral clustering. The embedding of the different manifolds can also be obtained from this matrix. We will show the improved performance of this algorithm on simulated as well as real hyperspectral reflectance data of two ternary mixtures with two shared endmembers.