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A common goal in biological sciences is to model a complex web of connections using a small number of interacting units. We present a general approach for dividing up elements in a spatial map based on their connectivity properties, allowing for the discovery of local regions underlying large-scale connectivity matrices. Our method is specifically designed to respect spatial layout and identify locally-connected clusters, corresponding to plausible coherent units such as strings of adjacent DNA base pairs, subregions of the brain, animal communities, or geographic ecosystems. Instead of using approximate greedy clustering, our nonparametric Bayesian model infers a precise parcellation using collapsed Gibbs sampling. We utilize an infinite clustering prior that intrinsically incorporates spatial constraints, allowing the model to search directly in the space of spatially-coherent parcellations. After showing results on synthetic datasets, we apply our method to both functional and structural connectivity data from the human brain. We find that our parcellation is substantially more effective than previous approaches at summarizing the brain's connectivity structure using a small number of clusters, produces better generalization to individual subject data, and reveals functional parcels related to known retinotopic maps in visual cortex. Additionally, we demonstrate the generality of our method by applying the same model to human migration data within the United States. This analysis reveals that migration behavior is generally influenced by state borders, but also identifies regional communities which cut across state lines. Our parcellation approach has a wide range of potential applications in understanding the spatial structure of complex biological networks.
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