Second-Order Pooling for Graph Neural Networks

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 45; no. 6; pp. 6870 - 6880
• Main Authors: Wang, Zhengyang, Ji, Shuiwang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Classification; Computer vision; Correlation; Covariance matrices; Deep learning; Graph neural networks; graph pooling; Graph representations; Graphical representations; Machine learning; Neural networks; Nodes; second-order statistics; Task analysis
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2020.2999032

Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.