Tensor State Space-based Dynamic Multilayer Network Modeling
This work addresses the challenge of understanding dynamic multilayer networks for scientific domains, representing an incremental improvement over existing models that fail to capture such dynamics.
The paper tackles the problem of modeling complex interactions in dynamic multilayer networks by introducing the Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), which captures temporal and cross-layer dynamics using a latent space framework with symmetric Tucker decomposition, and demonstrates its efficacy through numerical simulations and case studies.
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.