Hierarchical Manifold Clustering on Diffusion Maps for Connectomics (MIT 18.S096 final project)

In this paper, we introduce a novel algorithm for segmentation of imperfect boundary probability maps (BPM) in connectomics. Our algorithm can be a considered as an extension of spectral clustering. Instead of clustering the diffusion maps with traditional clustering algorithms, we learn the manifold and compute an estimate of the minimum normalized cut. We proceed by divide and conquer. We also introduce a novel criterion for determining if further splits are necessary in a component based on it's topological properties. Our algorithm complements the currently popular agglomeration approaches in connectomics, which overlook the geometrical aspects of this segmentation problem.