Graph-based two-sample tests and graph-based change-point detection that utilize a similarity graph provide a powerful tool for analyzing high-dimensional and non-Euclidean data as these methods do not impose distributional assumptions on data and have good performance across various scenarios. Current graph-based tests that deliver efficacy across a broad spectrum of alternatives typically reply on the $K$-nearest neighbor graph or the $K$-minimum spanning tree. However, these graphs can be vulnerable for high-dimensional data due to the curse of dimensionality. To mitigate this issue, we propose to use a robust graph that is considerably less influenced by the curse of dimensionality. We also establish a theoretical foundation for graph-based methods utilizing this proposed robust graph and demonstrate its consistency under fixed alternatives for both low-dimensional and high-dimensional data.

翻译：基于图的双样本检验和变点检测方法利用相似性图为分析高维和非欧几里得数据提供了有力工具，因为这些方法不对数据施加分布假设，并在各种场景下表现出良好性能。当前能在广泛备择假设下取得有效性的基于图检验通常依赖于$K$-近邻图或$K$-最小生成树。然而，由于维数灾难，这些图在高维数据中可能变得脆弱。为缓解该问题，我们提出使用一种受维数灾难影响显著减小的鲁棒图。我们还为利用该鲁棒图的基于图方法建立了理论基础，并证明了其在低维和高维数据固定备择假设下的一致性。