Graph Neural Networks (GNNs) are a highly effective neural network architecture for processing graph-structured data. Unlike traditional neural networks that rely solely on the features of the data as input, GNNs leverage both the graph structure, which represents the relationships between data points, and the feature matrix of the data to optimize their feature representation. This unique capability enables GNNs to achieve superior performance across various tasks. However, it also makes GNNs more susceptible to noise and adversarial attacks from both the graph structure and data features, which can significantly increase the training difficulty and degrade their performance. Similarly, a hypergraph is a highly complex structure, and partitioning a hypergraph is a challenging task. This paper leverages spectral adversarial robustness evaluation to effectively address key challenges in complex-graph algorithms. By using spectral adversarial robustness evaluation to distinguish robust nodes from non-robust ones and treating them differently, we propose a training-set construction strategy that improves the training quality of GNNs. In addition, we develop algorithms to enhance both the adversarial robustness of GNNs and the performance of hypergraph clustering. Experimental results show that this series of methods is highly effective.

翻译：图神经网络（GNNs）是一种处理图结构数据的高效神经网络架构。与传统神经网络仅依赖数据特征作为输入不同，GNNs同时利用表示数据点之间关系的图结构以及数据的特征矩阵来优化其特征表示。这一独特能力使GNNs能够在多种任务中取得优异性能。然而，这也使得GNNs更容易受到来自图结构和数据特征的噪声与对抗攻击的影响，从而显著增加训练难度并降低其性能。类似地，超图是一种高度复杂的结构，对超图进行划分是一项具有挑战性的任务。本文利用谱对抗鲁棒性评估来有效解决复杂图算法中的关键挑战。通过使用谱对抗鲁棒性评估区分鲁棒节点与非鲁棒节点并对其采取差异化处理，我们提出了一种训练集构建策略，以提升GNNs的训练质量。此外，我们开发了算法来同时增强GNNs的对抗鲁棒性和超图聚类的性能。实验结果表明，这一系列方法具有显著效果。