Abstract We consider the online monitoring of multivariate streaming data for changes that are characterized by an unknown subspace structure manifested in the covariance matrix. In particular, we consider the covariance structure changes from an identity matrix to an unknown spiked covariance model. We assume the postchange distribution is unknown and propose two detection procedures: the largest-eigenvalue Shewhart chart and the subspace-cumulative sum (CUSUM) detection procedure. We present theoretical approximations to the average run length (ARL) and the expected detection delay (EDD) for the largest-eigenvalue Shewhart chart and provide analysis for tuning parameters of the subspace-CUSUM procedure. The performance of the proposed methods is illustrated using simulation and real data for human gesture detection and seismic event detection.

中文翻译：

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顺序子空间变化点检测

摘要 我们考虑在线监测多元流数据的变化，这些变化的特征是协方差矩阵中出现的未知子空间结构。特别是，我们考虑了协方差结构从单位矩阵到未知尖峰协方差模型的变化。我们假设后变化分布未知，并提出两种检测程序：最大特征值休哈特图和子空间累积和 (CUSUM) 检测程序。我们给出了最大特征值 Shewhart 图的平均运行长度 (ARL) 和预期检测延迟 (EDD) 的理论近似值，并提供了子空间 CUSUM 程序调整参数的分析。使用用于人体手势检测和地震事件检测的模拟和真实数据来说明所提出方法的性能。