Sequential subspace change point detection

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.