This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for univariate time series. We propose applying random projections multiple times and then combining the univariate test results using existing multiple comparison methods. Simulation results suggest that the proposed method tends to have better size and power, with more accurate location estimation. At the same time, random projections may introduce variability in the estimated locations. To enhance stability in practice, we recommend repeating the procedure, and using the mode of the estimated locations as a guide for the final change point estimate. An application to an Australian temperature dataset is presented. This study, though limited to the single change point setting, demonstrates the usefulness of random projections in change point analysis.

翻译：本文提出了一种利用随机投影进行高维数据变点识别的新方法。通过将高维时间序列投影至一维空间，我们得以充分利用单变量时间序列分析的丰富文献。我们建议多次应用随机投影，然后使用现有的多重比较方法整合单变量检验结果。仿真研究表明，所提方法往往具有更好的检验水平和功效，且能获得更精确的位置估计。同时，随机投影可能会引入估计位置的可变性。为增强实际应用的稳定性，我们建议重复执行该流程，并以估计位置的众数作为最终变点估计的参考依据。本文以澳大利亚气温数据集为例进行了应用分析。本研究虽仅限于单变点场景，但证明了随机投影在变点分析中的实用价值。