提出新图聚类方法，解决高维数据中聚类失效问题。
Clustering with Uniformity- and Neighbor-Based Random Geometric Graphs
- 用邻近距离构建随机性检验，自动确定聚类半径。
- 在中等维度数据上表现稳定，优于传统方法。
- 适合复杂形状簇与均匀噪声背景，参数少易用。
我们提出一种基于聚类捕获图（CCDs）的图聚类方法，扩展其在中等维度数据中的适用性。现有变体如RK-CCDs依赖于基于Ripley's K函数的空间随机性检验，随维度增加性能下降。为此，我们引入基于最近邻距离（NND）的蒙特卡洛空间随机性检验（MC-SRT），用于确定覆盖半径，从而提出统一性与邻近性结合的CCDs（UN-CCDs）。该方法适用于中等规模和维度的数据集，尤其在簇结构复杂且背景噪声均匀分布的情形下表现良好。通过蒙特卡洛模拟和基准数据集实验，我们验证了UN-CCDs在评估范围内具备稳定且有竞争力的聚类性能，同时保持高度参数自由。我们也分析了计算开销，并明确了该方法最有效的实际应用场景。
原文摘要 · Abstract (English)
We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on Ripley's K function, which exhibit performance degradation as dimensionality increases. To address this limitation, we introduce a nearest-neighbor-distance (NND) based Monte Carlo spatial randomness test (MC-SRT) for determining covering radii, resulting in the proposed Uniformity- and Neighbor-based CCDs (UN-CCDs). The proposed method is designed for datasets of moderate size and dimension, particularly in settings with complex cluster geometry and uniformly distributed background noise. Through Monte Carlo simulations and experiments on benchmark datasets, we show that UN-CCDs provide stable and competitive performance relative to several established clustering methods within the evaluated regimes, while remaining largely parameter-free. We also discuss computational trade-offs and identify the practical regimes in which the method is most effective. -- Keywords: Graph-based clustering; Cluster catch digraphs; Moderate-dimensional data; the nearest neighbor distance; Spatial randomness test.
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