Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Simple Recursive Approach for Detecting Spatial Clusters

  • Kim Jeongjin (Department of Mathematics, Myongji University) ;
  • Chung Younshik (Department of Statistics, Pusan National University) ;
  • Ma Sungjoon (Department of Mathematics, Myongji University) ;
  • Yang Tae Young (Department of Mathematics, Myongji University)
  • Published : 2005.04.01
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Abstract

A binary segmentation procedure is a simple recursive approach to detect clusters and provide inferences for the study space when the shape of the clusters and the number of clusters are unknown. The procedure involves a sequence of nested hypothesis tests of a single cluster versus a pair of distinct clusters. The size and the shape of the clusters evolve as the procedure proceeds. The procedure allows for various growth clusters and for arbitrary baseline densities which govern the form of the hypothesis tests. A real tree data is used to highlight the procedure.

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References

  1. Breiman, L., Friedman J.H., Olshen, R.A., and Stone, C.J. (1984). Classification and Regression Trees. Wadworth and Brooks/Cole, Monterey
  2. Braun, J.V. and Muller, H. (1998). Statistical methods for DNA sequence segmentation. Statistical Science 13, 142-162 https://doi.org/10.1214/ss/1028905933
  3. Chen, J. and Gupta, A.K. (1997). Testing and Locating Variance Change points with Application to Stock Prices. Journal of the American Statistical Association 92, 739-747 https://doi.org/10.2307/2965722
  4. Cressie, N. (1993). Statistics for spacial data, second edition. Wiley, New York
  5. Kim, H. and Mallick, B.K. (2002). Analyzing spatial data using skew-Gaussian processes. In Spatial Cluster Modelling, A. Lawson and D. Denison (editors). Chapman and Hall, London, 163-173
  6. Raftery, A. (1995). Bayesian model selection in social research. Sociological methodology, ed. P. Marsden, Blackwell, Oxford
  7. Schlattmann, P., Gallinat, J., and Bohning, D. (2002). Spatio-temporal partition modelling: an example from neurophysiology. In Spatial Cluster Modelling, A. Lawson and D. Denison (editors). Chapman and Hall, London, 227-234
  8. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6, 461-464 https://doi.org/10.1214/aos/1176344136
  9. Scott, A.J. and Knott, M. (1974). A cluster analysis method for grouping means in the analysis of variance. Biometrics 30, 507-512 https://doi.org/10.2307/2529204
  10. Titterington, D.M., Smith, A.F.M., and Makov, U.E. (1985). Statistical Analysis of Finite Mixture Distributions. Wiley: New York
  11. van Dyk, D.A. and Hans, C.M. (2002). Accounting for absorption lines in images obtained with the Chandra X -ray Observatory. In Spatial Cluster Modelling, A. Lawson and D. Denison (editors). Chapman and Hall, London, 175-198
  12. Venkatraman, E.S. (1992). Consistency results in multiple change-point situations. Manuscript, Department of Statistics, Stanford University
  13. Vostrikova, L.J. (1981). Detecting 'disorder' in multidimensional random processes. Soviet Mathematics Doklady 24, 55-59
  14. Yang, T.Y. and Kuo, L. (2001). Bayesian binary segmentation procedure for a Poisson process with multiple changepoints. Journal of Computational and Graphical Statistics 10, 772-785 https://doi.org/10.1198/106186001317243449
  15. Yang, T.Y. (2004). Bayesian binary segmentation procedure for detecting streakiness in sports. Journal of the Royal Statistical Society Series A 167, 627-637 https://doi.org/10.1111/j.1467-985X.2004.00484.x
  16. Yang, T.Y. (2005). A tree-based model for homogeneous groupings of multinomials. Statistics in Medicine, in press
  17. Yang, T.Y. and Swartz, T. (2005). Applications of binary segmentation to the estimation of quantal response curves and spatial intensity. Biometrical Journal, in press