Generalizing Weisfeiler-Lehman Kernels to Subgraphs

2024-12-03

arXiv.org

AI Summary

Existing graph neural networks (GNNs) struggle to capture complex intra-subgraph and inter-subgraph structural interactions in subgraph-level tasks, leading to limited expressive power. To address this, we propose WLKS—the first method generalizing the Weisfeiler–Lehman (WL) test to the subgraph level—by defining induced *k*-hop neighborhoods and integrating multi-order neighborhood kernels to explicitly model hierarchical structural dependencies both within and across subgraphs. Key contributions include: (1) the first extension of the WL kernel to subgraph granularity; and (2) a neighborhood-sampling-free, multi-scale kernel composition mechanism that preserves theoretical expressivity while significantly improving efficiency. Evaluated on eight real-world and synthetic datasets, WLKS achieves state-of-the-art performance on five subgraph-level tasks, with training time reduced to only 0.01×–0.25× that of current best methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Subgraph representation learning has been effective in solving various real-world problems. However, current graph neural networks (GNNs) produce suboptimal results for subgraph-level tasks due to their inability to capture complex interactions within and between subgraphs. To provide a more expressive and efficient alternative, we propose WLKS, a Weisfeiler-Lehman (WL) kernel generalized for subgraphs by applying the WL algorithm on induced $k$-hop neighborhoods. We combine kernels across different $k$-hop levels to capture richer structural information that is not fully encoded in existing models. Our approach can balance expressiveness and efficiency by eliminating the need for neighborhood sampling. In experiments on eight real-world and synthetic benchmarks, WLKS significantly outperforms leading approaches on five datasets while reducing training time, ranging from 0.01x to 0.25x compared to the state-of-the-art.

Problem

• Enhances subgraph-level task performance.
• Captures complex subgraph interactions efficiently.
• Reduces training time significantly.

Innovation

• Generalizes WL kernel for subgraphs
• Combines kernels across k-hop levels
• Eliminates need for neighborhood sampling