Recent technological advances allow for the collection of massive data in the study of complex phenomena over time and/or space in various fields. Many of these data involve sequences of high-dimensional or non-Euclidean measurements, where change-point analysis is a crucial early step in understanding the data. Segmentation, or offline change-point analysis, divides data into homogeneous temporal or spatial segments, making subsequent analysis easier; its online counterpart detects changes in sequentially observed data, allowing for real-time anomaly detection. This article reviews a nonparametric change-point analysis framework that utilizes graphs representing the similarity between observations. This framework can be applied to data as long as a reasonable dissimilarity distance among the observations can be defined. Thus, this framework can be applied to a wide range of applications, from high-dimensional data to non-Euclidean data, such as imaging data or network data. In addition, analytic formulas can be derived to control the false discoveries, making them easy off-the-shelf data analysis tools.

中文翻译：

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基于图形的变化点分析


最近的技术进步允许在研究各个领域随时间和/或空间变化的复杂现象中收集大量数据。其中许多数据涉及高维或非欧几里得测量序列，其中变化点分析是理解数据的关键早期步骤。分割或离线变化点分析将数据划分为同质的时间或空间段，使后续分析更容易;其在线对应功能可检测顺序观察到的数据的变化，从而实现实时异常检测。本文回顾了一个非参数变化点分析框架，该框架利用表示观测值之间相似性的图形。只要可以定义观测值之间的合理相异距离，此框架就可以应用于数据。因此，该框架可以应用于广泛的应用，从高维数据到非欧几里得数据，例如成像数据或网络数据。此外，可以推导出分析公式来控制错误的发现，使它们成为简单的现成数据分析工具。