Doubly unfolded adjacency spectral embedding of dynamic multiplex graphs

TL;DR

This paper introduces a new latent position model for dynamic multiplex graphs and a spectral embedding method, DUASE, which efficiently captures complex temporal and layer-specific network behaviors.

Contribution

The paper proposes the DMPRDPG model and the DUASE spectral embedding method, enabling consistent, low-dimensional, and computationally efficient analysis of dynamic multiplex networks.

Findings

DUASE estimates are consistent and asymptotically normal.

The method captures time-specific and layer-specific effects effectively.

Applications demonstrate practical utility in real-world networks.

Abstract

Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot product graph (DMPRDPG), which uses an inner product between layer-specific and time-specific latent representations of the nodes to obtain edge probabilities. We further introduce a computationally efficient spectral embedding method for estimation of DMPRDPG parameters, called doubly unfolded adjacency spectral embedding (DUASE). The DUASE estimates are proved to be both consistent and asymptotically normally distributed. A key strength of our method is the encoding of time-specific node representations and layer-specific effects in separate latent spaces, which allows the model to capture complex behaviors while maintaining relatively low dimensionality. The embedding method we propose can also be efficiently used for subsequent inference tasks. In particular, we highlight the use of the ISOMAP algorithm in conjunction with DUASE as a way to efficiently capture trends and global changepoints within a network, and the use of DUASE for graph clustering. Applications on real-world networks describing geopolitical interactions between countries and financial news reporting demonstrate practical uses of our method.