Explainable Graph Representation Learning via Graph Pattern Analysis

TL;DR

This work addresses the gap in representation-level explainability for graph representations by introducing PXGL-EGK and PXGL-GNN, which analyze and learn graph representations through pattern analysis of substructures. The ensemble graph kernel framework combines multiple pattern kernels with learnable weights to deliver both accurate similarity measures and interpretable pattern contributions, while the GNN-based extension learns pattern representations from sampled subgraphs and fuses them into an explainable ensemble representation. The authors provide robustness and generalization guarantees and demonstrate superior performance and interpretability on benchmark datasets for both supervised and unsupervised tasks. Overall, the approach offers concrete insights into which graph patterns drive representations, enabling more trustworthy and domain-aligned graph learning.

Abstract

Explainable artificial intelligence (XAI) is an important area in the AI community, and interpretability is crucial for building robust and trustworthy AI models. While previous work has explored model-level and instance-level explainable graph learning, there has been limited investigation into explainable graph representation learning. In this paper, we focus on representation-level explainable graph learning and ask a fundamental question: What specific information about a graph is captured in graph representations? Our approach is inspired by graph kernels, which evaluate graph similarities by counting substructures within specific graph patterns. Although the pattern counting vector can serve as an explainable representation, it has limitations such as ignoring node features and being high-dimensional. To address these limitations, we introduce a framework (PXGL-GNN) for learning and explaining graph representations through graph pattern analysis. We start by sampling graph substructures of various patterns. Then, we learn the representations of these patterns and combine them using a weighted sum, where the weights indicate the importance of each graph pattern's contribution. We also provide theoretical analyses of our methods, including robustness and generalization. In our experiments, we show how to learn and explain graph representations for real-world data using pattern analysis. Additionally, we compare our method against multiple baselines in both supervised and unsupervised learning tasks to demonstrate its effectiveness.

Figures (4)

• Figure 1: Examples of graph patterns: $\mathcal{P}_{\text{path}}$, $\mathcal{P}_{\text{T}}$ and $\mathcal{P}_{\text{gl}}$
• Figure 2: t-SNE visualizations of PXGL-EGK's different kernel embeddings for the dataset PROTEINS.
• Figure 3: Framework of our proposed Pattern-based Explainable Graph Representation Learning with GNNs (PXGL-GNN)
• Figure 4: t-SNE visualizations of PXGL-GNN's pattern representations (supervised) for PROTEINS.

Theorems & Definitions (27)

• Definition 3.1: Pattern Counting Vector
• Definition 3.2: Pattern Counting Kernel
• Definition 3.3: Learnable Ensemble Kernel
• Definition 4.1: Pattern Sampling Set
• Definition 4.2: Pattern Representation
• Definition 4.3: Ensemble Representation
• Theorem 5.1
• Theorem 5.2
• Lemma C.1
• Lemma C.2: Inequalities