Uncovering migration systems through spatio-temporal tensor co-clustering.

A central problem in the study of human mobility is that of migration systems. Typically, migration systems are defined as a set of relatively stable movements of people between two or more locations over time. While these emergent systems are expected to vary over time, they ideally contain a stable underlying structure that could be discovered empirically. There have been some notable attempts to formally or informally define migration systems. However, they have been limited by being hard to operationalize and defining migration systems in ways that ignore origin/destination aspects and fail to account for migration dynamics over time. In this work, we propose to employ spatio-temporal tensor co-clustering-that stems from signal processing and machine learning theory-as a novel migration system analysis tool. Tensor co-clustering is designed to cluster entities exhibiting similar patterns across multiple modalities and thus suits our purpose of analyzing spatial migration activities across time. To demonstrate its effectiveness in describing stable migration systems, we first focus on domestic migration between counties in the US from 1990 to 2018. We conduct three case studies on domestic migration, namely, (i) US Metropolitan Areas, (ii) the state of California, and (iii) Louisiana, in which the last focuses on detecting exogenous events such as Hurricane Katrina in 2005. In addition, we also examine a case study at a larger scale, using worldwide international migration data from 200 countries between 1990 and 2015. Finally, we conclude with a discussion of this approach and its limitations.