Graph-based two-sample tests and graph-based change-point detection that utilize similarity graphs provide powerful tools for analyzing high-dimensional and non-Euclidean data as these methods do not impose distributional assumptions 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：基于相似性图的图基双样本检验和图基变点检测方法，为分析高维和非欧几里得数据提供了强大工具，因为这些方法无需假设分布，且在多种场景下均具有良好的性能。当前能够在广泛备选假设下有效工作的图基检验通常依赖$K$近邻图或$K$最小生成树。然而，受维度灾难影响，这些图在处理高维数据时可能较为脆弱。为解决此问题，我们提出使用一种受维度灾难影响显著较小的鲁棒图。我们进一步为采用该鲁棒图的图基方法奠定了理论基础，并证明了其在低维与高维数据固定备选假设下的一致性。