GNN-MgrPool: Enhanced graph neural networks with multi-granularity pooling for graph classification

Graph neural networks (GNNs) have gained sufficient attention and are applied to various domain tasks. At present, numerous pooling approaches are being proposed to aggregate node features and obtain node embeddings. However, current GNNs are black-box models that typically use a flat or single pooling step to aggregate nodes, which only considers the similarity between nodes within the cluster. These approaches ignore the influence of relationships within and between clusters in the learning process. To address this issue, we propose a novel multi-granular pooling method that aggregates nodes by simultaneously considering density and relationships among nodes and clusters. This method allows us to obtain multi-granular node-embedding clusters from GNN layers. The clusters in the current layer are built upon those in the previous layer, and these clusters change from fine to coarse as the number of clusters decreases during learning, which is achieved by using multi-granular pooling (MgrPool). Additionally, there is an inclusion relation between adjacent layers, and the node representation of each layer is established through the ratio of node distance within clusters to that between clusters. Finally, we conducted several experiments on node and graph classification tasks by combining GNN models with this pooling approach. The results demonstrate that our GNN-MgrPool model outperforms similar state-of-the-art algorithms and largely improves the interpretability of the learning process.