Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling

In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties; in turn, they are fundamental operators for building deep GNNs that learn effective, hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarsened versions of a graph by leveraging on its topology only. During training, the GNN learns new representations for the vertices and fits them to a pyramid of coarsened graphs, which is computed in a pre-processing step. As theoretical contributions, we first demonstrate the equivalence between the MAXCUT partition and the node decimation procedure on which NDP is based. Then, we propose a procedure to sparsify the coarsened graphs for reducing the computational complexity in the GNN; we also demonstrate that it is possible to drop many edges without significantly altering the graph spectra of coarsened graphs. Experimental results show that NDP grants a significantly lower computational cost once compared to state-of-the-art graph pooling operators, while reaching, at the same time, competitive accuracy performance on a variety of graph classification tasks.