  Following the success of convolution on non-Euclidean space, the
corresponding pooling approaches have also been validated on various tasks
regarding graphs. However, because of the fixed compression quota and stepwise
pooling design, these hierarchical pooling methods still suffer from local
structure damage and suboptimal problem. In this work, inspired by structural
entropy, we propose a hierarchical pooling approach, SEP, to tackle the two
issues. Specifically, without assigning the layer-specific compression quota, a
global optimization algorithm is designed to generate the cluster assignment
matrices for pooling at once. Then, we present an illustration of the local
structure damage from previous methods in the reconstruction of ring and grid
synthetic graphs. In addition to SEP, we further design two classification
models, SEP-G and SEP-N for graph classification and node classification,
respectively. The results show that SEP outperforms state-of-the-art graph
pooling methods on graph classification benchmarks and obtains superior
performance on node classifications.
