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

We propose {\delta}-MAPS, a method that analyzes spatio-temporal data to first identify the distinct spatial components of the underlying system, referred to as "domains", and second to infer the connections between them. A domain is a spatially contiguous region of highly correlated temporal activity. The core of a domain is a point or subregion at which a metric of local homogeneity is maximum across the entire domain. We compute a domain as the maximum-sized set of spatially contiguous cells that include the detected core and satisfy a homogeneity constraint, expressed in terms of the average pairwise cross-correlation across all cells in the domain. Domains may be spatially overlapping. Different domains may have correlated activity, potentially at a lag, because of direct or indirect interactions. The proposed edge inference method examines the statistical significance of each lagged cross-correlation between two domains, infers a range of lag values for each edge, and assigns a weight to each edge based on the covariance of the two domains. We illustrate the application of {\delta}-MAPS on data from two domains: climate science and neuroscience.