Spatial and temporal clustering based on the echelon scan technique and software analysis


In this paper, we propose the details of algorithms for the echelon and the echelon scan techniques for the first time though we have already proposed these techniques through specific numerical examples in previous papers. We also release EcheScan software developed in R and Shiny-server based on this algorithm. Through an internet browser, researchers can access the technologies in web applications. We discuss the clustering and hotspot detection for spatial and temporal lattice data. Our approach is based on the idea of echelon techniques. The echelon dendrogram is a powerful tool to handle any types of lattice data with visualization. Regional features such as hotspots and trends are shown in an echelon dendrogram. The echelon scan technique searches for a hotspot by moving the scanning window in a particular manner. The echelon scan technique is easy to interpret based on regional hierarchical structure of interested values according to visual order. We propose the algorithms to obtain the elements for echelon and the maximum likelihood ratio based on echelon scan given the values of lattice and its neighbors. We also explain the usages of EcheScan software for echelon and echelon scanning. In addition, the echelon technique for two types of lattice data and spatio-temporal epidemiological lung cancer data in New Mexico are illustrated using EcheScan software.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. Cressie, N. (1993). Statistics for spatial data. New York: Wiley.

    Google Scholar 

  2. Cressie, N., & Chan, N. H. (1989). Spatial modelling of regional variables. Journal of the American Statistical Association, 84, 393–401.

    MathSciNet  Article  Google Scholar 

  3. Gelfand, A. E., Diggle, P. J., Fuentes, M., & Guttorp, P. (Eds.). (2010). Handbook of spatial statistics. Boca Raton: Chapman & Hall.

    Google Scholar 

  4. Huang, L., Kulldorff, M., & Gregorio, D. (2007). A spatial scan statistic for survival data. Biometrics, 63(1), 109–118.

    MathSciNet  Article  Google Scholar 

  5. Ishioka, F., & Kurihara, K. (2012). Detection of spatial clustering using echelon scan. In A. Colubi, (eds) Proceedings of the 20th international conference on computational statistics (COMPSTAT2012) (pp. 341–352). Heidelberg: Physica-Verlag.

  6. Ishioka, F., Kawahara, J., Mizuta, M., Minato, S., & Kurihara, K. (2019). Evaluation of hotspot cluster detection using spatial scan statistic based on exact counting. Japanese Journal of Statistics and Data and Science, 2(1), 241–262.

    MathSciNet  Article  Google Scholar 

  7. Ishioka, F., Kurihara, K., Suito, H., Horikawa, Y., & Ono, Y. (2007). Detection of hotspots for 3-dimensional spatial data and its application to environmental pollution data. Journal of Environmental Science for Sustainable Society, 1, 15–24.

    Article  Google Scholar 

  8. Kulldorff, M., & Harvard Medical School, Boston and Information Management Services Inc. (2018). SaTScan™v9.6: Software for the spatial and space-time scan statistics. Accessed 1 July 2018.

  9. Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics: Theory and Methods, 26(6), 1481–1496.

    MathSciNet  Article  Google Scholar 

  10. Kulldorff, M., Feuer, E. J., Miller, B. A., Athas, W. F., & Key, C. R. (1998). Evaluating cluster alarms: A space-time scan statistic and brain cancer in Los Alamos. American Journal of Public Health, 88, 1377–1380.

    Article  Google Scholar 

  11. Kulldorff, M., Huang, L., & Konty, K. (2009). A scan statistic for continuous data based on the normal probability model. International Journal of Health Geographics, 8, 58.

    Article  Google Scholar 

  12. Kulldorff, M., & Nagarwalla, N. (1995). Spatial disease clusters: Detection and inference. Statistics in Medicine, 14(8), 799–810.

    Article  Google Scholar 

  13. Kurihara, K. (2003). The detection of hotspots based on the hierarchical spatial structure. Bulletin of the Computational Statistics of Japan, 15(2), 171–183.

    Google Scholar 

  14. Kurihara, K. (2004). Classification of geospatial lattice data and their graphical Representation. In D. Banks (Ed.), Classification, clustering, and data mining applications (pp. 251–258). Berlin: Springer.

    Google Scholar 

  15. Kurihara, K., Ishioka, F., & Moon, S. (2006). Detection of Hotspots on Spatial Data by Using Principal Component Analysis. Journal of the Korean Data Analysis Society, 8(2), 447–458.

    Google Scholar 

  16. Kurihara, K., Myers, W. L., & Patil, G. P. (2000). Echelon analysis of the relationship between population and land cover patterns based on remote sensing data. Community Ecology, 1, 103–122.

    Article  Google Scholar 

  17. Myers, W. L., Kurihara, K., Patil, G. P., & Vraney, R. (2006). Finding upper level sets in cellular surface data using echelons and SaTScan. Environmental and Ecological Statistics, 13(4), 379–390.

    MathSciNet  Article  Google Scholar 

  18. Myers, W. M., Patil, G. P., & Joly, K. (1997). Echelon approach to areas of concern in synoptic regional monitoring. Environmental and Ecological Statistics, 4, 131–152.

    Article  Google Scholar 

  19. Myers, W. M., Patil, G. P., & Taillie, C. (1999). Conceptualizing pattern analysis of spectral change relative to ecosystem status. Ecosystem Health, 5, 285–293.

    Article  Google Scholar 

  20. Patil, G. P., & Taillie, C. (2004). Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environmental and Ecological Statistics, 11(2), 183–197.

    MathSciNet  Article  Google Scholar 

  21. Takahashi, K., Yokoyama, T., & Tango, T. (2010). FleXScan v3.1.2: Software for the flexible scan statistic. Tokyo: National Institute of Public Health Japan.

    Google Scholar 

  22. Tango, T., & Takahashi, K. (2005). A flexible spatial scan statistic for detecting clusters. International Journal of Health Geographics, 4, 11.

    Article  Google Scholar 

  23. Tango, T., & Takahashi, K. (2012). A flexible spatial scan statistic with a restricted likelihood ratio for detecting disease clusters. Statistics in Medicine, 31(30), 4207–4218.

    MathSciNet  Article  Google Scholar 

  24. Tomita, M., Hatsumichi, M., & Kurihara, K. (2008). Identify LD blocks based on hierarchical spatial data. Computational Statistics and Data Analysis, 52(4), 1806–1820.

    MathSciNet  Article  Google Scholar 

Download references


The authors thank the Editor and the two referees for their sharp and constructive comments. This work was partly supported by JSPS KAKENHI Grant Number JP17K0005009.

Author information



Corresponding author

Correspondence to Koji Kurihara.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Appendix 1: Input and output values of Algorithms 1–3

See Tables 3, 4 and 5.

Table 3 Input and output values of Algorithm 1
Table 4 Input and output values of Algorithm 2
Table 5 Input and output values of Algorithm 3

Appendix 2: Input and output files of EcheScan

See Tables 6.

Table 6 Input and output files of EcheScan

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kurihara, K., Ishioka, F. & Kajinishi, S. Spatial and temporal clustering based on the echelon scan technique and software analysis. Jpn J Stat Data Sci 3, 313–332 (2020).

Download citation


  • Echelon analysis
  • Spatial clustering
  • Spatial scan statistic
  • R language and Shiny software
  • Web application
  • EcheScan software