Change-point detection (CPD) involves identifying distributional changes in a sequence of independent observations. Among nonparametric methods, rank-based methods are attractive due to their robustness and effectiveness and have been extensively studied for univariate data. However, they are not well explored for high-dimensional or non-Euclidean data. This paper proposes a new method, Rank INduced by Graph Change-Point Detection (RING-CPD), which utilizes graph-induced ranks to handle high-dimensional and non-Euclidean data. The new method is asymptotically distribution-free under the null hypothesis, and an analytic $p$-value approximation is provided for easy type-I error control. Simulation studies show that RING-CPD effectively detects change-points across a wide range of alternatives and is also robust to heavy-tailed distribution and outliers. The new method is illustrated by the detection of seizures in a functional connectivity network dataset and travel pattern changes in the New York City Taxi dataset.

翻译：变点检测（CPD）涉及识别独立观测序列中的分布变化。在非参数方法中，基于秩的方法因其鲁棒性和有效性而备受关注，并已在一元数据中得到广泛研究。然而，这些方法在高维或非欧几里得数据中的应用尚不充分。本文提出了一种新方法——基于图诱导秩的变点检测（RING-CPD），该方法利用图诱导秩来处理高维和非欧几里得数据。新方法在原假设下具有渐近分布无关性，并提供了分析性 $p$ 值近似方法以便于控制第一类错误。模拟研究表明，RING-CPD 能够有效检测各种备择假设下的变点，并且对重尾分布和异常值具有鲁棒性。通过在功能连接网络数据集中检测癫痫发作以及纽约市出租车数据集中出行模式变化，进一步展示了该方法的实际应用效果。