  Graph pooling is a crucial operation for encoding hierarchical structures
within graphs. Most existing graph pooling approaches formulate the problem as
a node clustering task which effectively captures the graph topology.
Conventional methods ask users to specify an appropriate number of clusters as
a hyperparameter, then assume that all input graphs share the same number of
clusters. In inductive settings where the number of clusters can vary, however,
the model should be able to represent this variation in its pooling layers in
order to learn suitable clusters. Thus we propose GMPool, a novel
differentiable graph pooling architecture that automatically determines the
appropriate number of clusters based on the input data. The main intuition
involves a grouping matrix defined as a quadratic form of the pooling operator,
which induces use of binary classification probabilities of pairwise
combinations of nodes. GMPool obtains the pooling operator by first computing
the grouping matrix, then decomposing it. Extensive evaluations on molecular
property prediction tasks demonstrate that our method outperforms conventional
methods.
