High-dimensional changepoint analysis is a growing area of research and has applications in a wide range of fields. The aim is to accurately and efficiently detect changepoints in time series data when both the number of time points and dimensions grow large. Existing methods typically aggregate or project the data to a smaller number of dimensions, usually one. We present a high-dimensional changepoint detection method that takes inspiration from geometry to map a high-dimensional time series to two dimensions. We show theoretically and through simulation that if the input series is Gaussian, then the mappings preserve the Gaussianity of the data. Applying univariate changepoint detection methods to both mapped series allows the detection of changepoints that correspond to changes in the mean and variance of the original time series. We demonstrate that this approach outperforms the current state-of-the-art multivariate changepoint methods in terms of accuracy of detected changepoints and computational efficiency. We conclude with applications from genetics and finance.

中文翻译：

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通过几何启发式映射进行高维变化点检测

高维变化点分析是一个不断发展的研究领域，并在广泛的领域中得到了应用。目的是当时间点的数量和维度都变大时，准确而有效地检测时间序列数据中的变化点。现有方法通常将数据聚合或投影到较小数量的维度（通常是一个维度）。我们提出了一种高维变化点检测方法，该方法从几何学中汲取灵感，将高维时间序列映射到二维。我们从理论上通过仿真显示，如果输入序列为高斯，则映射将保留数据的高斯性。将单变量变化点检测方法应用于两个映射序列都可以检测到与原始时间序列的均值和方差变化相对应的变化点。我们证明，该方法在检测到的变更点的准确性和计算效率方面优于当前最新的多元变更点方法。我们以遗传学和金融学的应用结尾。