From spatio-temporal data to a weighted and lagged network between functional domains: Applications in climate and neuroscience
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Spatio-temporal data have become increasingly prevalent and important for both science and enterprises. Such data are typically embedded in a grid with a resolution larger than the true dimensionality of the underlying system. One major task is to identify the distinct semi-autonomous functional components of the spatio-temporal system and to infer their interconnections. In this thesis, we propose two methods that identify the functional components of a spatio-temporal system. Next, an edge inference process identifies the possibly lagged and weighted connections between the system’s components. The weight of an edge accounts for the magnitude of the interaction between two components; the lag associated with each edge accounts for the temporal ordering of these interactions. The first method, geo-Cluster, infers the spatial components as “areas”; spatially contiguous, non-overlapping, sets of grid cells satisfying a homogeneity constraint in terms of their average pair-wise cross-correlation. However, in real physical systems the underlying physical components might overlap. To this end we also propose δ-MAPS, a method that first identifies the epicenters of activity of the functional components of the system and then creates domains – spatially contiguous, possibly overlapping, sets of grid cells that satisfy the same homogeneity constraint. The proposed framework is applied in climate science and neuroscience. We show how these methods can be used to evaluate cutting edge climate models and identify lagged relationships between different climate regions. In the context of neuroscience, the method successfully identifies well-known “resting state networks” as well as a few areas forming the backbone of the functional cortical network. Finally, we contrast the proposed methods to dimensionality reduction techniques (e.g., clustering PCA/ICA) and show their limitations.