Simultaneous clustering and embedding for multiple intimate mixtures

Classical unmixing algorithms focus primarily on scenarios with a single mixture. These techniques are easily extensible in the case of images with multiple discrete mixtures (i.e. no shared endmembers). Unmixing in scenarios with multiple mixtures with shared or common endmembers is significantly harder. Manifold clustering and embedding seem tailor-made for such a scenario, but generally these algorithms focus on intersecting manifolds (i.e. manifolds that pass through each other) rather than adjoining manifolds (i.e. manifolds that share a boundary) as is the case with mixtures. In this paper we propose a NNMF based technique for simultaneous manifold clustering and embedding of adjoining manifolds. The algorithm is based on including a clustering term in the objective for finding an appropriate reconstruction matrix. The performance of the new algorithm is tested on a toy dataset made of a couple of simulated manifolds which share a boundary and a simulated dataset made up of two ternary Hapke mixtures with two shared endmembers. The algorithm shows improvements on the state-of-the-art manifold clustering algorithms in terms of both clustering and embedding.