δ -MAPS: from spatio-temporal data to a weighted and lagged network between functional domains.

In real physical systems the underlying spatial components might not have crisp boundaries and their interactions might not be instantaneous. To this end, we propose δ -MAPS; a method that identifies spatially contiguous and possibly overlapping components referred to as domains , and identifies the lagged functional relationships between them. Informally, a domain is a spatially contiguous region that somehow participates in the same dynamic effect or function. The latter will result in highly correlated temporal activity between grid cells of the same domain. δ -MAPS first identifies the epicenters of activity of a domain. Next, it identifies a domain as the maximum possible set of spatially contiguous grid cells that include the detected epicenters and satisfy a homogeneity constraint. After identifying the domains, δ -MAPS infers a functional network between them. The proposed network inference method examines the statistical significance of each lagged correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge reflecting the magnitude of interaction between two domains. δ -MAPS is related to clustering, multivariate statistical techniques and network community detection. However, as we discuss and also show with synthetic data, it is also significantly different, avoiding many of the known limitations of these methods. We illustrate the application of δ -MAPS on data from two domains: climate science and neuroscience. First, the sea-surface temperature climate network identifies some well-known teleconnections (such as the lagged connection between the El Nin õ Southern Oscillation and the Indian Ocean). Second, the analysis of resting state fMRI cortical data confirms the presence of known functional resting state networks (default mode, occipital, motor/somatosensory and auditory), and shows that the cortical network includes a backbone of relatively few regions that are densely interconnected.
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