SPGNN: Recognizing Salient Subgraph Patterns via Enhanced Graph Convolution and Pooling

TL;DR

SPGNN tackles the expressivity gap in neighborhood aggregation for graph classification by introducing a concatenation-based injective graph convolution (Cat-Agg) and a layer-wise WL-SortPool pooling that captures salient subgraph patterns across multiple scales. The Cat-Agg operation injectively updates node representations, while WL-SortPool sorts and preserves multi-layer node embeddings to form a comprehensive graph representation $Z_G$. Empirical results on standard benchmarks show SPGNN achieving competitive or state-of-the-art performance against graph kernels and other DL methods, with ablations validating the contributions of both components. The approach enables end-to-end learning of discriminative subgraph patterns and offers robust, permutation-invariant graph representations.

Abstract

Graph neural networks (GNNs) have revolutionized the field of machine learning on non-Euclidean data such as graphs and networks. GNNs effectively implement node representation learning through neighborhood aggregation and achieve impressive results in many graph-related tasks. However, most neighborhood aggregation approaches are summation-based, which can be problematic as they may not be sufficiently expressive to encode informative graph structures. Furthermore, though the graph pooling module is also of vital importance for graph learning, especially for the task of graph classification, research on graph down-sampling mechanisms is rather limited. To address the above challenges, we propose a concatenation-based graph convolution mechanism that injectively updates node representations to maximize the discriminative power in distinguishing non-isomorphic subgraphs. In addition, we design a novel graph pooling module, called WL-SortPool, to learn important subgraph patterns in a deep-learning manner. WL-SortPool layer-wise sorts node representations (i.e. continuous WL colors) to separately learn the relative importance of subtrees with different depths for the purpose of classification, thus better characterizing the complex graph topology and rich information encoded in the graph. We propose a novel Subgraph Pattern GNN (SPGNN) architecture that incorporates these enhancements. We test the proposed SPGNN architecture on many graph classification benchmarks. Experimental results show that our method can achieve highly competitive results with state-of-the-art graph kernels and other GNN approaches.

Figures (3)

• Figure 1: Motivation for the layer-wise sort-pooling module (left) and architecture of SPGNN (right). In the left figure, the input vertices are illustrated as colored nodes. Suppose that the relative importance of rooted subtrees in the same layer is decided by their sizes, node 6 is more important than node 1 in the first layer, while node 1 plays a more important structural role in the second layer. The right figure shows key components of SPGNN that are explained below.
• Figure 2: Illustration of WL-SortPool: In each layer/iteration, the proposed graph convolution updates the node representations. After that, WL-SortPool learns node importance. Node representations in the current layer are sorted and pooled accordingly.
• Figure 3: Visualization of layer-wisely pooled nodes based on the IMDB-M dataset.

Theorems & Definitions (2)

• Proposition 1
• Theorem 2