Tensor State Space-based Dynamic Multilayer Network Modeling

TL;DR

This paper introduces TSSDMN, a tensor state space model that captures temporal and cross-layer dynamics in complex multilayer networks using a Tucker decomposition and variational inference.

Contribution

The paper presents a novel tensor state space model with a Tucker decomposition framework for dynamic multilayer networks, enabling better modeling of temporal and layer interactions.

Findings

TSSDMN effectively captures intra- and inter-layer dynamics.

The model demonstrates superior performance in simulations and case studies.

Efficient inference achieved via variational EM algorithm.

Abstract

Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper introduces a novel Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), utilizing a latent space model framework. TSSDMN employs a symmetric Tucker decomposition to represent latent node features, their interaction patterns, and layer transitions. Then by fixing the latent features and allowing the interaction patterns to evolve over time, TSSDMN uniquely captures both the temporal dynamics within layers and across different layers. The model identifiability conditions are discussed. By treating latent features as variables whose posterior distributions are approximated using a mean-field variational inference approach, a variational Expectation Maximization algorithm is developed for efficient model inference. Numerical simulations and case studies demonstrate the efficacy of TSSDMN for understanding dynamic multilayer networks.