IRWE: Inductive Random Walk for Joint Inference of Identity and Position Network Embedding

TL;DR

An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized.

Abstract

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. Most existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk (RW) on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. We demonstrate that some RW statistics can characterize node identities and positions while supporting the inductive inference. Experiments validate the superior performance of IRWE over various baselines for the transductive and inductive inference of identity and position embeddings.

Figures (5)

• Figure 1: An example of identity and position embedding in terms of (b) struc2vec and (c) node2vec, where each color denotes a unique identity while nodes in the same community have similar positions.
• Figure 2: Model architecture of IRWE including modules of (b) identity and (c) position embeddings.
• Figure 3: Running examples about the derivation of one-hot AW encodings $\{ \rho (\omega) \}$, AW statistics $\{ s (v)\}$, and high-order degree features $\{ \delta (v) \}$ based on the local topology of node $v_1$ in Fig. \ref{['Fig:Graph-Exp']}.
• Figure 4: Parameter analysis w.r.t. $l$, $\alpha$, and $\tau$ on PPI in terms of F1-score$\uparrow$ (node position classification) and NCut$\downarrow$ (node identity clustering).
• Figure 5: Parameter analysis w.r.t. $l$, $\alpha$, and $\tau$ on USA in terms of F1-score$\uparrow$ (node identity classification) and modularity$\uparrow$ (community detection).