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Uncovering migration systems through spatio-temporal tensor co-clustering

Zack W. Almquist, Tri Duc Nguyen, Mikael Sorensen, Xiao Fu, Nicholas D. Sidiropoulos

TL;DR

This work proposes to employ spatio-temporal tensor co-clustering—that stems from signal processing and machine learning theory—as a novel migration system analysis tool, designed to cluster entities exhibiting similar patterns across multiple modalities and suits its purpose of analyzing spatial migration activities across time.

Abstract

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 by defining migration systems in ways that ignore origin/destination aspects and/or fail to account for migration dynamics. In this work we propose a novel method, spatio-temporal (ST) tensor co-clustering, stemming from signal processing and machine learning theory. To demonstrate its effectiveness for describing stable migration systems we focus on domestic migration between counties in the US from 1990-2018. Relevant data for this period has been made available through the US Internal Revenue Service. Specifically, we concentrate on three illustrative case studies: (i) US Metropolitan Areas, (ii) the state of California, and (iii) Louisiana, focusing on detecting exogenous events such as Hurricane Katrina in 2005. Finally, we conclude with discussion and limitations of this approach.

Uncovering migration systems through spatio-temporal tensor co-clustering

TL;DR

This work proposes to employ spatio-temporal tensor co-clustering—that stems from signal processing and machine learning theory—as a novel migration system analysis tool, designed to cluster entities exhibiting similar patterns across multiple modalities and suits its purpose of analyzing spatial migration activities across time.

Abstract

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 by defining migration systems in ways that ignore origin/destination aspects and/or fail to account for migration dynamics. In this work we propose a novel method, spatio-temporal (ST) tensor co-clustering, stemming from signal processing and machine learning theory. To demonstrate its effectiveness for describing stable migration systems we focus on domestic migration between counties in the US from 1990-2018. Relevant data for this period has been made available through the US Internal Revenue Service. Specifically, we concentrate on three illustrative case studies: (i) US Metropolitan Areas, (ii) the state of California, and (iii) Louisiana, focusing on detecting exogenous events such as Hurricane Katrina in 2005. Finally, we conclude with discussion and limitations of this approach.
Paper Structure (8 sections, 7 equations, 15 figures)

This paper contains 8 sections, 7 equations, 15 figures.

Table of Contents

  1. Comparison with alternative methods
  2. Comparison with prior works
  3. IRS Data
  4. International Migration Data
  5. Spatial-Temporal Co-clustering Model
  6. Algorithm, Software, and Hyperparameter Selection
  7. Comparison methods: Walktrap
  8. Comparison method: InfoMAP

Figures (15)

  • Figure 1: 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, ${\bf a}(1)$ (San Francisco) and ${\bf a}(2)$ (Santa Clara) are nonzero. The destinations are Alameda, San Mateo, and Marin, and thus the corresponding ${\bf b}(j)$'s ($j=3,4,5$) are nonzero---as shown in the lower subfigure. In addition, the top table shows ${\bf a} {\bf b}^T$, i.e., the spatial association of transmitters and receivers. The migration intensity is the ${\bf c}$ 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 such spatio-temporal rank-one terms.
  • Figure 2: Spatial and temporal plots of US Metro origin and destination migration systems. (a) Significant origin MSAs; (b) Significant destination MSAs; (c) temporal (intensity) profile of the migration system; (d) matrix representation of the migration system with inclusion with origin on the rows and destination on the columns; and (e) Sankey diagram of this migration system.
  • Figure 3: Major origin and destination migration systems (networks) for California Counties. The six tiles represent the six most important communities in relation to sending and receiving over 1990 to 2018. (a) Significant origin and destination counties in Community 1 (b) Significant origin and destination counties in Community 2; (c) Significant origin and destination counties in Community 3; (d) Significant origin and destination counties in Community 4; (e) Significant origin and destination counties in Community 5; and (f) Significant origin and destination counties in Community 6.
  • Figure 4: For each of the six communities in Figure \ref{['fig:California_COM']} there is a temporal profile for the "intensity" of the migration system over time. This allows us to see how active this migration system is at different time periods. (a) Temporal intensity profile for Community 1 (b) Temporal intensity profile for Community 2; (c) Temporal intensity profile for Community 3; (d) Temporal intensity profile for Community 4; (e) Temporal intensity profile for Community 5; and (f) Temporal intensity profile for Community 6.
  • Figure 5: These two plots show a fully classified California for origin/destination migration systems under a three system model. (a) Sender (origin) migration systems (3 Community solution); and (b) receiver (destination) migration systems (3 Community solution).
  • ...and 10 more figures