CCP-GNN: Competitive Covariance Pooling for Improving Graph Neural Networks

Graph neural networks (GNNs) have advanced graph classification tasks, where a global pooling to generate graph representations by summarizing node features plays a critical role in the final performance. Most of the existing GNNs are built with a global average pooling (GAP) or its variants, which however, take no full consideration of node specificity while neglecting rich statistics inherent in node features, limiting classification performance of GNNs. Therefore, this article proposes a novel competitive covariance pooling (CCP) based on observation of graph structures, i.e., graphs generally can be identified by a (small) key part of nodes. To this end, our CCP generates node-level second-order representations to explore rich statistics inherent in node features, which are fed to a competitive-based attention module for effectively discovering key nodes through learning node weights. Subsequently, our CCP aggregates node-level second-order representations in conjunction with node weights by summation to produce a covariance representation for each graph, while an iterative matrix normalization is introduced to consider geometry of covariances. Note that our CCP can be flexibly integrated with various GNNs (namely CCP-GNN) to improve the performance of graph classification with little computational cost. The experimental results on seven graph-level benchmarks show that our CCP-GNN is superior or competitive to state-of-the-arts. Our code is available at https://github.com/Jillian555/CCP-GNN.