{\delta}-MAPS: From spatio-temporal data to a weighted and lagged network between functional domains

TL;DR

{ extdelta}-MAPS is a novel method for analyzing spatio-temporal data that identifies spatially contiguous domains and infers their lagged, weighted connections, with applications demonstrated in climate science and neuroscience.

Contribution

The paper introduces { extdelta}-MAPS, a new approach for detecting domains and their interactions in spatio-temporal data, including lagged and weighted connections.

Findings

Successfully identified spatial domains in climate and neuroscience data.

Inferred significant lagged and weighted connections between domains.

Demonstrated applicability across different scientific fields.

Abstract

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.