Sequential Subspace Changepoint Detection
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We consider the sequential changepoint detection problem of detecting changes that are characterized by a subspace structure which is manifested in the covariance matrix. In particular, the covariance structure changes from an identity matrix to an unknown spiked covariance model. We consider three sequential changepoint detection procedures: The exact cumulative sum (CUSUM) that assumes knowledge of all parameters, the largest eigenvalue procedure and a novel Subspace-CUSUM algorithm with the last two being used for the case when unknown parameters are present. By leveraging the extreme eigenvalue distribution from random matrix theory and modeling the non-negligible temporal correlation in the sequence of detection statistics due to the sliding window approach, we provide theoretical approximations to the average run length (ARL) and the expected detection delay (EDD) for the largest eigenvalue procedure. The three methods are compared to each other using simulations.
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