Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks
This work addresses the problem of improving structural pattern analysis in graph data for researchers and practitioners in graph representation learning, though it appears incremental as it builds on existing disentangled and kernel-based approaches.
The paper tackled the limitation of existing disentangled graph representation methods in implicitly and coarsely characterizing graph structures by proposing the Graph Optimal Matching Kernel Convolutional Network (GOMKCN), which achieved superior accuracy and interpretability in graph pattern mining and prediction.
Graphs effectively characterize relational data, driving graph representation learning methods that uncover underlying predictive information. As state-of-the-art approaches, Graph Neural Networks (GNNs) enable end-to-end learning for diverse tasks. Recent disentangled graph representation learning enhances interpretability by decoupling independent factors in graph data. However, existing methods often implicitly and coarsely characterize graph structures, limiting structural pattern analysis within the graph. This paper proposes the Graph Optimal Matching Kernel Convolutional Network (GOMKCN) to address this limitation. We view graphs as node-centric subgraphs, where each subgraph acts as a structural factor encoding position-specific information. This transforms graph prediction into structural pattern recognition. Inspired by CNNs, GOMKCN introduces the Graph Optimal Matching Kernel (GOMK) as a convolutional operator, computing similarities between subgraphs and learnable graph filters. Mathematically, GOMK maps subgraphs and filters into a Hilbert space, representing graphs as point sets. Disentangled representations emerge from projecting subgraphs onto task-optimized filters, which adaptively capture relevant structural patterns via gradient descent. Crucially, GOMK incorporates local correspondences in similarity measurement, resolving the trade-off between differentiability and accuracy in graph kernels. Experiments validate that GOMKCN achieves superior accuracy and interpretability in graph pattern mining and prediction. The framework advances the theoretical foundation for disentangled graph representation learning.