Graph Probabilistic Pooling: From Bernoulli to Poisson Distribution.

Abstract

Graph pooling is crucial for enlarging the receptive field and reducing computational costs in deep graph representation learning. In this work, we propose a simple but effective graph probabilistic pooling (GP-Pool) framework to facilitate graph feature learning. Instead of either deterministic selection or random dropping, we design a probabilistic subgraph sampling to reach an expected distribution by deducing a variational bound. Accordingly, a Bernoulli graph pooling (BernPool) is first derived to sample nodes together with the local structures, for which a learnable reference set is introduced to encode nodes into a latent expressive probability space. Hereby, the resultant BernPool captures salient graph substructures while possessing much diversity on sampled nodes due to its nondeterministic manner. For more controllable pooling, we derive the Poisson-distributed version (aka PoissonPool) from BernPool to explicitly cut the node quantity with less variables in variational learning. Furthermore, considering the complementarity of node sampling and clustering, we propose a hybrid graph pooling (HGP) paradigm to combine a compact subgraph (via BernPool/PoissonPool) and a coarsening graph (via clustering), to retain both representative substructures and global topology. Extensive experiments on multiple public graph classification datasets demonstrate that our GP-Pool is superior to various graph pooling methods and achieves state-of-the-art performance.