Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling

24 Oct 2019  ·  Filippo Maria Bianchi, Daniele Grattarola, Lorenzo Livi, Cesare Alippi ·

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.

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification 5pt. Bench-Easy NDP Accuracy 97.9 # 1
Graph Classification Bench-hard NDP Accuracy 72.6 # 1
Graph Classification COLLAB NDP Accuracy 79.1% # 17
Graph Classification D&D NDP Accuracy 72% # 42
Graph Classification ENZYMES NDP Accuracy 43.9% # 37
Graph Classification MUTAG NDP Accuracy 84.7% # 62
Graph Classification Mutagenicity NDP Accuracy 78.1 # 4
Graph Classification NCI1 NDP Accuracy 73.5% # 43
Graph Classification PROTEINS Graph2Vec Accuracy 73.3% # 79
Graph Classification REDDIT-B NDP Accuracy 84.3 # 8


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