HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-ange relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-in-play module for improving the representational power of HGCNNs. Specifically, HERALD adaptively optimizes the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned. Furthermore, HERALD employs the self-attention mechanism to capture the non-local paired-nodes relation. Extensive experiments on various popular hypergraph datasets for node classification and graph classification tasks demonstrate that our approach obtains consistent and considerable performance enhancement, proving its effectiveness and generalization ability.

中文翻译：

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用于超图学习的可学习超图拉普拉斯算子

超图卷积神经网络 (HGCNN) 已经证明了它们在对图结构化数据中保留的高阶关系进行建模方面的潜力。然而，大多数现有的卷积滤波器都是由预定义的初始超图拓扑局部化和确定的，而忽略了探索现实世界数据中的隐式和长程关系。在本文中，我们提出了第一种为构建自适应超图结构量身定制的基于学习的方法，称为 HypERgrAph Laplacian 适配器（HERALD），它作为通用插件模块，用于提高 HGCNN 的表示能力。具体来说，HERALD 以端到端的方式自适应地优化超节点和超边之间的邻接关系，从而学习任务感知超图。此外，HERALD 采用自注意力机制来捕获非本地配对节点关系。在用于节点分类和图分类任务的各种流行的超图数据集上进行的大量实验表明，我们的方法获得了一致且可观的性能增强，证明了其有效性和泛化能力。