GeoExplainer: Interpreting Graph Convolutional Networks with geometric masking

Abstract

For Graph Convolutional Network (GCN), the inherent geometric topology and relationships within spatio-temporal graphs are critical to factors affect its predictive performance. Understanding the decision-making process of GCN remains a challenging task. Existing perturbation-based explanation methods are primarily tailored for Graph Neural Network (GNN) models and focus on how the information of nodes or subgraphs in static graphs impacts GNN predictions. Due to the geometric properties of spatio-temporal graphs, screw theory serves as crucial mathematical tools for describing the geometric relationships and patterns of motion within the geometric space of spatio-temporal graphs. Therefore,we propose GeoExplainer, which utilizes screw theory to geometric masking for spatio-temporal graphs with strong geometric correlations, generating explanations for GCN. Our method perturbs spatio-temporal graphs using geometric masking, and ultimately generating explanations in the form of geometric masks serve as importance mappings for model prediction results. Firstly, we design a screw motion vector model with geometric constraints to describe the spatio-temporal graph in screw system. Then, we design a geometric screw perturbation to generate smooth geometric masks. Finally, we propose a geometric masking approach to optimize and update the geometric mixture mask. We utilize pointwise mutual information (PMI) to maximize the correlation between the model predictions after geometric perturbation and the original predictions, obtaining the optimal geometric mask as an explanation for GCN. The interpretable experiments of ST-GCN, HD-GCN, GCN and GIN models on four datasets with geometric relationships demonstrate that GeoExplainer outperforms eight competitive interpretation methods in quantitative and visualization analysis.