Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling

TL;DR

This paper introduces Node Decimation Pooling (NDP), a novel graph pooling method that creates coarser graphs efficiently while maintaining topology, improving computational efficiency and performance in graph neural networks.

Contribution

The paper proposes NDP, a new pooling operator for GNNs that uses spectral partitioning and Kron reduction to generate efficient, topologically-preserving coarser graphs.

Findings

NDP outperforms state-of-the-art pooling methods in efficiency.

NDP achieves competitive accuracy on various graph classification tasks.

NDP reduces computational costs significantly.

Abstract

In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties, and they are fundamental for building deep GNNs that learn hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarser graphs while preserving the overall graph topology. During training, the GNN learns new node representations and fits them to a pyramid of coarsened graphs, which is computed offline in a pre-processing stage. NDP consists of three steps. First, a node decimation procedure selects the nodes belonging to one side of the partition identified by a spectral algorithm that approximates the \maxcut{} solution. Afterwards, the selected nodes are connected with Kron reduction to form the coarsened graph. Finally, since the resulting graph is very dense, we apply a sparsification procedure that prunes the adjacency matrix of the coarsened graph to reduce the computational cost in the GNN. Notably, we show that it is possible to remove many edges without significantly altering the graph structure. Experimental results show that NDP is more efficient compared to state-of-the-art graph pooling operators while reaching, at the same time, competitive performance on a significant variety of graph classification tasks.