응용통계연구 (The Korean Journal of Applied Statistics)

  • 제34권1호
  • /
  • Pages.25-38
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  • 2021
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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동적 DCSBM을 모니터링하는 자기출발 절차

Self-starting monitoring procedure for the dynamic degree corrected stochastic block model

  • 이주원 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Lee, Joo Weon (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 투고 : 2020.10.05
  • 심사 : 2020.11.04
  • 발행 : 2021.02.28
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초록

최근 동적 연결망의 비정상적 변화를 감시하기 위한 연결망 모니터링의 필요성이 높아지고 있다. 이 논문에서는 연결망의 구조적 변화를 감시하기 위한 동적 연결망의 모형으로 DCSBM(degree corrected stochastic block model)을 고려하였다. 관리도 절차를 사용하여 동적 연결망을 감시하려면 제1국면을 통해 초기 연결망을 확보한 후 모형의 모수를 추정하는 단계를 거쳐야 한다. 그러나 연결망의 감시에서는 충분한 수의 초기 연결망을 확보하기 어려운 경우가 대부분이다. 이 논문에서는 동적 DCSBM을 감시하기 위한 자기출발 관리도 절차를 제안한다. 이 절차는 모형의 모수 추정을 위해 확보한 연결망의 수가 아주 적은 경우에 유용하게 사용할 수 있는 절차이다. 모의실험을 통해 절차의 성능을 평가한 결과, 제안된 절차는 초기 연결망의 수가 아주 적은 경우에도 좋은 관리상태의 성능을 나타내는 것을 알 수 있었다.

Recently the need for network surveillance to detect abnormal behavior within dynamic social networks has increased. We consider a dynamic version of the degree corrected stochastic block model (DCSBM) to simulate dynamic social networks and to monitor for a significant structural change in these networks. To apply a control charting procedure to network surveillance, in-control model parameters must be estimated from the Phase I data, that is from historical data. In network surveillance, however, there are many situations where sufficient relevant historical data are unavailable. In this paper we propose a self-starting Shewhart control charting procedure for detecting change in the dynamic networks. This procedure can be a very useful option when we have only a few initial samples for parameter estimation. Simulation results show that the proposed procedure has good in-control performance even when the number of initial samples is very small.

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과제정보

이 논문은 2019년도 중앙대학교 연구 장학기금 지원에 의한 것임.

참고문헌

  1. Capizzi, G. and Masarotto, G. (2010). Self-starting CUSCORE control charts for individual multivariate observations, Journal of Quality Technology, 42, 136-151. https://doi.org/10.1080/00224065.2010.11917812
  2. Hawkins, D. M. (1987). Self-starting CUSUM charts for location and scale, The Statistician, 36, 299-315. https://doi.org/10.2307/2348827
  3. Hawkins, D. M. and Maboudou-Tchao, E. M. (2007). Self-starting multivariate exponentially weighted moving average control charting, Technometrics, 49, 199-209. https://doi.org/10.1198/004017007000000083
  4. Hawkins, D. M. and Olwell, D. H. (1998). Cumulative sum charts and charting for quality improvement, New York, Springer.
  5. Karrer, B. and Newman, M. E. J. (2011). Stochastic blockmodels and community structure in networks, Physical Review E, 83, 016107. https://doi.org/10.1103/physreve.83.016107
  6. Keefe, M. J., Woodall, W. H., and Jones-Farmer, L. A. (2015). The conditional in-control performance of self-starting control charts, Quality Engineering, 27, 488-499. https://doi.org/10.1080/08982112.2015.1065323
  7. Lee, J. W., Kim, M., and Lee, J. (2018). The in-control performance of self-starting EWMA and X charts, Journal of the Korean Data & Information Science Society, 29, 851-860. https://doi.org/10.7465/jkdi.2018.29.4.851
  8. Priebe, C. E., Conroy, J. M., Marchette, D. J., and Park, Y. (2005). Scan statistics on Enron graphs, Computational and Mathematical Organization Theory, 11, 229-247. https://doi.org/10.1007/s10588-005-5378-z
  9. Qin, T. and Rohe, K. (2013). Regularized spectral clustering under the degree-corrected stochastic block model, Advances in Neural Information Processing Systems, 3120-3128.
  10. Quesenberry, C. P. (1991a). SPC Q charts for a binomial parameter p: Short or long runs, Journal of Quality Technology, 23, 239-246. https://doi.org/10.1080/00224065.1991.11979329
  11. Quesenberry, C. P. (1991b). SPC Q charts for a Poisson parameter λ: Short or long runs, Journal of Quality Technology, 23, 296-303. https://doi.org/10.1080/00224065.1991.11979345
  12. Quesenberry, C. P. (1995). Geometric Q charts for high quality processes, Journal of Quality Technology, 27, 304-315. https://doi.org/10.1080/00224065.1995.11979610
  13. Sengupta, S. and Chen, Y. (2015). Spectral clustering in heterogeneous networks, Statistica Sinica, 25, 1081-1106.
  14. Shen, X., Tsui, K. L., Zou, C., and Woodall, W. H. (2016). Self-starting monitoring scheme for Poisson count data with varying population sizes, Technometrics, 58, 460-471. https://doi.org/10.1080/00401706.2015.1075423
  15. Shetty, J. and Adibi, J. (2005). Discovering important nodes through graph entropy the case of Enron email database, Proceeding of the 3rd international workshop on Link discovery, 74-81.
  16. Sullivan, J. H. and Jones, L. A. (2002). A self-starting control chart for multivariate individual observations, Technometrics, 44, 24-33. https://doi.org/10.1198/004017002753398290
  17. Wilson, J. D., Stevens, N. T., and Woodall, W. H. (2019). Modeling and detecting change in temporal networks via a dynamic degree corrected stochastic block model, Quality and Reliability Engineering International, 35, 1363-1378. https://doi.org/10.1002/qre.2520
  18. Yu, L., Woodall, W. H., and Tsui, K. L. (2018). Detecting node propensity changes in the dynamic degree corrected stochastic block model, Social Networks, 54, 209-227. https://doi.org/10.1016/j.socnet.2018.03.004
  19. Yu, L., Zwetsloot, I. M., Stevens, N. T., Wilson, J. D., and Tsui, K. L. (2020). Monitoring dynamic networks: a simulation-based strategy for comparing monitoring methods and a comparative study, submitted to a journal for publication.
  20. Zhang, M., Peng, Y., Schuh, A., Megahed, F. M., and Woodall, W. H. (2013). Geometric charts with estimated control limits. Quality and Reliability Engineering International, 29, 209-223. https://doi.org/10.1002/qre.1304