标题： 低秩变化的顺序检测使用极值特征值 显示英文标题

标题： Sequential detection of low-rank changes using extreme eigenvalues

摘要： 我们研究了检测信号协方差矩阵突然变化的问题。特别是，协方差从“白色”单位矩阵变为未知的尖峰或低秩矩阵。提出了两种基于样本协方差矩阵最大和最小特征值的顺序变点检测程序。为了控制虚警率，我们通过利用随机矩阵理论中的极值特征值分布，并通过捕获滑动窗口方法导致的扫描统计量序列中不可忽略的时间相关性，给出了检测平均运行长度（ARL）和期望检测延迟（EDD）的精确理论近似。真实数据示例展示了我们的方法在检测群体行为变化方面的良好性能。 显示英文摘要

摘要： We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sample covariance matrix. To control false-alarm-rate, we present an accurate theoretical approximation to the average-run-length (ARL) and expected detection delay (EDD) of the detection, leveraging the extreme eigenvalue distributions from random matrix theory and by capturing a non-negligible temporal correlation in the sequence of scan statistics due to the sliding window approach. Real data examples demonstrate the good performance of our method for detecting behavior change of a swarm.