Given that no existing graph construction method can generate a perfect graph for a given dataset, graph-based algorithms are invariably affected by the plethora of redundant and erroneous edges present within the constructed graphs. In this paper, we propose treating these noisy edges as adversarial attack and use a spectral adversarial robustness evaluation method to diminish the impact of noisy edges on the performance of graph algorithms. Our method identifies those points that are less vulnerable to noisy edges and leverages only these robust points to perform graph-based algorithms. Our experiments with spectral clustering, one of the most representative and widely utilized graph algorithms, reveal that our methodology not only substantially elevates the precision of the algorithm but also greatly accelerates its computational efficiency by leveraging only a select number of robust data points.

翻译：鉴于现有图构建方法无法为给定数据集生成完美图，图基算法不可避免地受到构建图中大量冗余和错误边的影响。本文提出将这些噪声边视为对抗攻击，并采用频谱对抗鲁棒性评估方法来降低噪声边对图算法性能的影响。该方法能够识别受噪声边影响较小的数据点，仅利用这些鲁棒点执行图基算法。我们在最具代表性且广泛使用的图算法——谱聚类上的实验表明，所提方法不仅显著提升了算法的精确度，而且通过仅利用少数鲁棒数据点大幅加速了其计算效率。