Fig. 1
From: Uncovering migration systems through spatio-temporal tensor co-clustering
An example of the rank-one tensor-based representation of a stable migration system with its temporal profile. In this system, the origins are San Francisco and Santa Clara. Hence, \({\textbf{a}}(1)\) (San Francisco) and \({\textbf{a}}(2)\) (Santa Clara) are nonzero. The destinations are Alameda, San Mateo, and Marin, and thus, the corresponding \({\textbf{b}}(j)\)’s (\(j=3,4,5\)) are nonzero—as shown in the lower subfigure. In addition, the top table shows \({\textbf{a}} {\textbf{b}}^T\), i.e., the spatial association of transmitters and receivers. The migration intensity is the \({\textbf{c}}\) vector, which reflects how this system’s activity level varies over the years. When multiple migration systems are simultaneously present, the associated data tensor is described by a sum of spatio-temporal rank-one terms.
