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Graph pooling has been increasingly considered for graph neural networks(GNNs) to facilitate hierarchical graph representation learning. Existing graphpooling methods commonly consist of two stages, i.e., selecting the top-rankednodes and removing the rest nodes to construct a coarsened graphrepresentation. However, local structural information of the removed nodeswould be inevitably dropped in these methods, due to the inherent coupling ofnodes (location) and their features (signals). In this paper, we propose anenhanced three-stage method via lifting, named LiftPool, to improvehierarchical graph representation by maximally preserving the local structuralinformation in graph pooling. LiftPool introduces an additional stage of graphlifting before graph coarsening to preserve the local information of theremoved nodes and decouple the processes of node removing and featurereduction. Specifically, for each node to be removed, its local information isobtained by subtracting the global information aggregated from its neighboringpreserved nodes. Subsequently, this local information is aligned and propagatedto the preserved nodes to alleviate information loss in graph coarsening.Furthermore, we demonstrate that the proposed LiftPool is localized andpermutation-invariant. The proposed graph lifting structure is general to beintegrated with existing downsampling-based graph pooling methods. Evaluationson benchmark graph datasets show that LiftPool substantially outperforms thestate-of-the-art graph pooling methods in the task of graph classification.

LiftPool: Lifting-based Graph Pooling for Hierarchical Graph Representation Learning