[Paper Review] RiWalk: Fast Structural Node Embedding via Role Identification

Xuewei Ma, Geng Qin+3 more|arXiv (Cornell University)|Oct 15, 2019

Advanced Graph Neural Networks26 references7 citations

TL;DR

RiWalk is a novel framework for fast structural node embedding that decouples role identification from network embedding, using rooted kernel construction to preserve structural dependencies. It achieves state-of-the-art performance with up to 10x faster training than baselines while enabling effective transfer learning across diverse networks.

ABSTRACT

Nodes performing different functions in a network have different roles, and these roles can be gleaned from the structure of the network. Learning latent representations for the roles of nodes helps to understand the network and to transfer knowledge across networks. However, most existing structural embedding approaches suffer from high computation and space cost or rely on heuristic feature engineering. Here we propose RiWalk, a flexible paradigm for learning structural node representations. It decouples the structural embedding problem into a role identification procedure and a network embedding procedure. Through role identification, rooted kernels with structural dependencies kept are built to better integrate network embedding methods. To demonstrate the effectiveness of RiWalk, we develop two different role identification methods named RiWalk-SP and RiWalk-WL respectively and employ random walk based network embedding methods. Experiments on within-network classification tasks show that our proposed algorithms achieve comparable performance with other baselines while being an order of magnitude more efficient. Besides, we also conduct across-network role classification tasks. The results show potential of structural embeddings in transfer learning. RiWalk is also scalable, making it capable of capturing structural roles in massive networks.

Motivation & Objective

• Address the limitations of existing structural node embedding methods that suffer from high computational cost or reliance on heuristic feature engineering.
• Enable effective transfer learning of structural roles across networks of varying sizes and topologies.
• Decouple structural representation learning into role identification and network embedding procedures for modularity and efficiency.
• Develop a flexible framework that integrates graph kernel principles with modern network embedding techniques to improve scalability and performance.
• Demonstrate robustness and generalization of structural embeddings across diverse real-world networks, including infrastructure and social networks.

Proposed method

• Decompose structural node embedding into two stages: role identification and network embedding, enabling modular design and reuse of existing methods.
• Construct rooted kernels by relabeling context nodes based on their structural roles in the anchor node’s local subgraph, preserving structural dependencies.
• Propose two role identification methods: RiWalk-SP, based on neighbor degree similarity for shortest-path substructures; and RiWalk-WL, using neighborhood aggregation inspired by Weisfeiler-Lehman kernels for fine-grained patterns.
• Apply standard random walk-based network embedding methods (e.g., node2vec) on the relabeled subgraphs to learn structural node representations.
• Use biased random walks in the relabeled graphs to enhance exploration of structurally equivalent nodes, improving embedding quality.
• Leverage negative sampling and language model training for efficient optimization of the final embeddings.

Figure 1: Two nodes $a$ and $u$ residing far apart in a network have similar local topologies but totally different context nodes. However, after the role identification procedure, they have similar context and are indirectly densely connected, thus typical network embedding methods can be directly

Experimental results

Research questions

• RQ1 Can a decoupled framework combining role identification and network embedding achieve better efficiency and performance than end-to-end structural embedding methods?
• RQ2 To what extent can structural node embeddings learned via RiWalk generalize across networks of different sizes and types (e.g., infrastructure vs. social networks)?
• RQ3 How do RiWalk-SP and RiWalk-WL compare to state-of-the-art methods like struc2vec in terms of accuracy and computational efficiency?
• RQ4 Can RiWalk effectively capture structural roles such as structural holes and hubs, and how does it perform in transfer learning scenarios?
• RQ5 What is the scalability of RiWalk on large-scale networks, and how does its runtime grow with network size?

Key findings

• RiWalk-SP and RiWalk-WL achieve comparable or better performance than state-of-the-art baselines on within-network node classification tasks, with up to 10x faster training times.
• On the Europe:USA and USA:Actor cross-network transfer tasks, RiWalk-SP and RiWalk-WL outperform baselines significantly, showing robustness despite distribution shifts.
• RiWalk-WL achieves a 28.7% improvement over struc2vec on the Europe network and a 17.2% gain on the USA network in within-network classification.
• In structural hole identification, RiWalk-SP and RiWalk-WL achieve 145% and 127% performance gains over struc2vec on the Actor network, respectively.
• RiWalk-WL scales super-linearly with network size, with a complexity of approximately O(n^1.2), demonstrating strong scalability on Erdos-Renyi graphs up to 1 million nodes.
• The framework successfully captures structural roles across diverse networks—infrastructure (Europe, USA) and social (Actor)—indicating universality of structural roles regardless of network type or scale.

(a) Expressway network