Spectrally Similar Graph Pooling

We consider the problem of learning compositional hierarchies of graphs. Even though structural characteristics of graphs can be learned by Graph Neural Networks (GNNs), it is difficult to find an overall compositional hierarchy using such flat operators. In this paper, we propose a new graph pooling algorithm, Spectrally Similar Graph Pooling (SSGPool), to learn hierarchical representations of graphs. The main idea of the proposed SSGPool algorithm is to learn a coarsening matrix which maps nodes from an original graph to a smaller number of nodes in a coarsened graph. The coarsening matrix is trained to coarsen the nodes based on their feature vectors while keeping the spectral characteristics of the original graph in the coarsened one. Although existing graph pooling methods take either feature-based pooling or structure-preserving pooling, SSGPool considers two properties simultaneously in an end-to-end manner. Experiments on various graph benchmarks show the advantage of our method compared to strong baselines. To further investigate the effectiveness of our proposed method, we evaluate our approach on a real-world problem, image retrieval with visual scene graphs. Quantitative and qualitative analyses on the retrieval problem confirm that the proposed method efficiently captures the hierarchical semantic structure of scene graphs.