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.
KeywordsReliability Scan statistics Spatio-temporal surveillance Statistical process control (SPC) Statistical computing
This material is based upon work supported by NSF under Grants CMMI-1538746.
- Bartram J, Ballance R (1996) Water quality monitoring: a practical guide to the design and implementation of freshwater quality studies and monitoring programmes. CRC Press, New YorkGoogle Scholar
- Guerriero M, Willett P, Glaz J (2009) Distributed target detection in sensor networks using scan statistics. In: IEEE transactions on signal processing, vol. 57, pp 2629–2639Google Scholar
- Hotelling, H (1947) “Multivariate quality control,” Techniques of statistical analysisGoogle Scholar
- Liu K, Zhang R, Mei Y (2016) Scalable SUM-Shrinkage Schemes for Distributed Monitoring Large-Scale Data Streams. arXiv:1603.08652
- Mishin D, Brantner-Magee K, Czako F, Szalay AS (2014) “Real time change point detection by incremental PCA in large scale sensor data,” In: High performance extreme computing conference (HPEC), 2014 IEEE. IEEE pp 1–6Google Scholar
- Ripley BD (2005) Spatial statistics, vol 575. Wiley, New YorkGoogle Scholar
- Rogerson PA, Yamada I (2004) Approaches to syndromic surveillance when data consist of small regional counts. Morbidity and Mortality Weekly Report pp 79–85Google Scholar
- Xie, Y, Wang M, Thompson A (2015) Sketching for sequential change-point detection. In: 2015 IEEE global conference on signal and information processing (GlobalSIP), IEEE, pp 78–82Google Scholar
- Zhang F (2006) The Schur complement and its applications, vol 4. Springer, New YorkGoogle Scholar