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

  • Junzhuo Chen
  • Chuljin Park
  • Seong-Hee KimEmail author
  • Yao Xie
Article

Abstract

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.

Keywords

Reliability Scan statistics Spatio-temporal surveillance Statistical process control (SPC) Statistical computing 

Notes

Acknowledgements

This material is based upon work supported by NSF under Grants CMMI-1538746.

Supplementary material

10651_2019_425_MOESM1_ESM.pdf (800 kb)
Supplementary material 1 (pdf 799 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Junzhuo Chen
    • 1
  • Chuljin Park
    • 2
  • Seong-Hee Kim
    • 1
    Email author
  • Yao Xie
    • 1
  1. 1.H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Industrial EngineeringHanyang UniversitySeoulSouth Korea

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