## Topology-Aware Graph Signal Sampling for Pooling in Graph Neural Networks

### Abstract

As a generalization of convolutional neural networks to graph-structured data, graph convolutional networks learn feature embeddings based on the information of each node’s local neighborhood. However, due to the inherent irregularity of such data, extracting hierarchical representations of a graph becomes a challenging task. Several pooling approaches have been introduced to address this issue. In this paper, we propose a novel topology-aware graph signal sampling method to specify the nodes that represent the communities of a graph. Our method selects the sampling set based on the local variation of the signal of each node while considering vertex-domain distances of the nodes in the sampling set. In addition to the interpretability of the sampled nodes provided by our method, the experimental results both on stochastic block models and real-world dataset benchmarks show that our method achieves competitive results compared to the state-of-the-art in the graph classification task.

### Keywords

graph neural networks, pooling layer, graph signal sampling, graph classification

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