Demystifying Graph Neural Networks with Graph Filter Assessment

Graph Neural Networks (GNNs) have recently received tremendous attention due to their power in handling graph data for different downstream tasks across different application domains. Many GNN models have been proposed, which mainly differ in their graph filter design with the hope to find the best filter for all the graph data. However, there still lack studies on graph filter assessment from a data perspective. In particular, we raise the following three questions: (1) Whether there exists an optimal filter that performs the best on all graph data; (2) Which graph properties should be considered for finding the optimal graph filter; and (3) How to design appropriate filters that adapt to a given graph. In this paper, we focus on addressing the above questions, using semi-supervised node classification task as a case study. We propose a novel assessment tool: Graph Filter Discriminant Score (GFD), for evaluating the effectiveness of graph filters for a given graph in terms of node classification. Using this tool, we find out that there is no single filter that performs the best on all possible graphs, and graphs with different properties are in favor of different graph filters. Based on these findings, we develop Adaptive Filter Graph Neural Network (AFGNN), a simple but powerful model that can adaptively learn data-specific filters. For a given graph, AFGNN leverages graph filter assessment as an extra loss term and learns to combine a set of base filters. Experiments on both synthetic and real-world benchmark datasets have demonstrated that our proposed model has the flexibility in learning a data-specific filter and can consistently provide competitive performance across all the datasets.