Latent Space Models for Dynamic Networks

Abstract

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. We propose Markov chain Monte Carlo (MCMC) algorithm to estimate the model parameters and latent positions of the actors in the network. The model yields meaningful visualization of dynamic networks, giving the researcher insight into the evolution and the structure, both local and global, of the network. The model handles directed or undirected edges, easily handles missing edges, and lends itself well to predicting future edges. Further, a novel approach is given to detect and visualize an attracting influence between actors using only the edge information. We use the case-control likelihood approximation to speed up the estimation algorithm, modifying it slightly to account for missing data. We apply the latent space model to data collected from a Dutch classroom, and a cosponsorship network collected on members of the U.S. House of Representatives, illustrating the usefulness of the model by making insights into the networks. Supplementary materials for this article are available online.

• Embedding
• Markov chain Monte Carlo
• Network data
• Social influence
• Visualization

Additional information

Notes on contributors

Daniel K. Sewell

Daniel K. Sewell is Ph.D Candidate (E-mail: [email protected]), and Yuguo Chen is Associate Professor (E-mail: [email protected]), Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820. This work was supported in part by National Science Foundation grant DMS-11-06796. The authors thank the editor, the associate editor, and a referee for valuable suggestions.

Yuguo Chen

Daniel K. Sewell is Ph.D Candidate (E-mail: [email protected]), and Yuguo Chen is Associate Professor (E-mail: [email protected]), Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820. This work was supported in part by National Science Foundation grant DMS-11-06796. The authors thank the editor, the associate editor, and a referee for valuable suggestions.