Graph neural networks have emerged as a popular and powerful tool for learning hierarchical representation of graph data. In complement to graph convolution operators, graph pooling is crucial for extracting hierarchical representation of data in graph neural networks. However, most recent graph pooling methods still fail to efficiently exploit the geometry of graph data. In this paper, we propose a novel graph pooling strategy that leverages node affinity to improve the hierarchical representation learning of graph data. Node affinity is computed by harmonizing the kernel representation of topology information and node features. In particular, a structure-aware kernel representation is introduced to explicitly exploit advanced topological information for efficient graph pooling without eigendecomposition of the graph Laplacian. Similarities of node signals are evaluated using the Gaussian radial basis function (RBF) in an adaptive way. Experimental results demonstrate that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.

中文翻译：

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具有节点亲和力的图数据的多尺度表示学习

图神经网络已经成为学习图数据的分层表示的一种流行而强大的工具。作为图卷积运算符的补充，图池对于提取图神经网络中数据的层次表示形式至关重要。但是，最新的图形池化方法仍然无法有效利用图形数据的几何形状。在本文中，我们提出了一种新颖的图池化策略，该策略利用节点亲和力来改善图数据的分层表示学习。节点相似性是通过协调拓扑信息和节点特征的内核表示来计算的。特别是，引入了一种结构感知的内核表示形式，以明确利用高级拓扑信息进行有效的图形池化，而无需对图拉普拉斯算子进行特征分解。使用高斯径向基函数（RBF）以自适应方式评估节点信号的相似性。实验结果表明，所提出的图池化策略能够在一组公共图分类基准数据集上实现最新性能。