Hierarchical-Graph-Structured Edge Partition Models for Learning Evolving Community Structure

TL;DR

A novel dynamic network model is proposed to capture evolving latent communities within temporal networks that enables the inferred community structure to merge, split, and interact with one another, providing a comprehensive understanding of complex network dynamics.

Abstract

We propose a novel dynamic network model to capture evolving latent communities within temporal networks. To achieve this, we decompose each observed dynamic edge between vertices using a Poisson-gamma edge partition model, assigning each vertex to one or more latent communities through \emph{nonnegative} vertex-community memberships. Specifically, hierarchical transition kernels are employed to model the interactions between these latent communities in the observed temporal network. A hierarchical graph prior is placed on the transition structure of the latent communities, allowing us to model how they evolve and interact over time. Consequently, our dynamic network enables the inferred community structure to merge, split, and interact with one another, providing a comprehensive understanding of complex network dynamics. Experiments on various real-world network datasets demonstrate that the proposed model not only effectively uncovers interpretable latent structures but also surpasses other state-of-the art dynamic network models in the tasks of link prediction and community detection.

Figures (9)

• Figure 1: The left plot illustrates the data mapping across the three layers in our model, G-HSEPM. The bottom layer represents the observations, where some vertices are connected by edges. In the middle layer, vertices with strong connections naturally form communities. The top layer further groups these communities into hierarchical clusters based on their interactions. To clarify the relationships within each layer, we decompose the data at each stage in the middle plot. The right plot shows how the model operates across these layers: the blue section captures vertex-level memberships, while the pink section models community-level memberships.
• Figure 2: The comparisons of the model performance in terms of missing links prediction.
• Figure 3: Dynamic community detection on the synthetic dataset. (a) is the generated dynamic network, whose community structure is evolving with time ordered from top to bottom. (b), (c), (d), (e) and (f) are link probability inferred by G-HSEPM, HSEPM, DPGM, D-NGPPF and EPM, respectively. (g) shows how each vertex is allocated to communities of G-HSEPM at each time. (h) is the transition matrix of G-HSEPM, showing the interactions between communities.
• Figure 4: Dynamic community detection on vdBunt dataset. (a) shows the true networks. (b) depicts the networks inferred by our G-HSEPM model. We can find the inferred graph structure is aligned with the true graph. (c) illustrates how the normalised weights $r_{k}^{(t)} / (\sum_{t}r_{k}^{(t)})$ of the top 3 communities and the number of links between their corresponding major vertices change over time. The red, blue and green colours represent the top communities 2, 5, and 9, respectively. Dotted lines represent the number of links, and the colour-filled areas represent the normalised community weights.
• Figure 5: The latent graph structure of DBLP dataset inferred by G-HSEPM.