To reduce or not to reduce: a study on spatio-temporal surveillance

The majority of control charts based on scan statistics for spatio-temporal surveillance use full observation vectors. In high-dimensional applications, dimension-reduction techniques are usually applied. Typically, the dimension reduction is conducted as a post-processing step rather than in the data acquisition stage and thus, a full sample covariance matrix is required. When the dimensionality of data is high, (i) the sample covariance matrix tends to be ill-conditioned due to a limited number of samples; (ii) the inversion of such a sample covariance matrix causes numerical issues; and (iii) aggregating information from all variables may lead to high communication costs in sensor networks. In this paper, we propose a set of reduced-dimension (RD) control charts that perform dimension reduction during the data acquisition process by spatial scanning. The proposed methods avoid computational difficulties and possibly high communication costs. We derive a theoretical measure that characterizes the performance difference between the RD approach and the full observation approach. The numerical results show that the RD approach has little performance loss under several commonly used spatial models while enjoying all the benefits of implementation. A case study on water quality monitoring demonstrates the effectiveness of the proposed methods in real applications.