Unifying Structural Proximity and Equivalence for Enhanced Dynamic Network Embedding

TL;DR

This work tackles dynamic network embedding by jointly preserving structural proximity and structural equivalence while accounting for inter-snapshot dynamics. It introduces dynamic graphlets to define node roles via Dynamic Graphlet Degree Vectors (D-GDV) and builds a structural similarity network S; a temporal-structural random walk then samples time-respecting sequences that reflect both temporal proximity and structural similarity, controlled by a tunable $\alpha$. Embeddings are learned with Skip-Gram on these sequences, with performance measured on five real-world networks showing state-of-the-art results and revealing dataset-specific balances between proximity and equivalence. The approach offers a flexible and interpretable framework for dynamic networks, enabling robust node representations across tasks like classification and community detection, and suggests avenues for supervised tuning and spectral enhancements.

Abstract

Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network.

Figures (3)

• Figure 1: (a) All static graphlets with up to four nodes. Each graphlet has its unique automorphism orbits denoted in different colors, e.g. $G_0$ has one unique orbit, shown in black, while $G_3$ has two unique orbits shown in black and white. (b) All dynamic graphlets with up to three events. Automorphism orbits are shown in different colors. Ordered events of each graphlets are labeled with numbers where multiple events can occur on the same edge as labeled by numbers separated by commas.
• Figure 2: Dynamic Graphlet Degree Vectors (D-GDV) are extracted from the input network $G$ to construct a structural similarity network $S$. Temporal-structural random walks are then employed to sample time-respecting sequences of nodes, while considering both temporal proximity and structural similarity. Finally, the Skip-Gram model is employed to learn node embeddings from the sequences.
• Figure 3: Average Precision for different values of hyperparameter $\alpha$, where the vertical lines represent the standard deviation.