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Multivariate Spatial Cluster Analysis Using Mahalanobis Distance

  • Journal of the Korean Cartographic Association
  • Abbr : JKCA
  • 2012, 12(2), pp.37-46
  • Publisher : The Korean Cartographic Association
  • Research Area : Social Science > Geography > Geography in general > Cartography

Monghyeon Lee 1

1University of Texas at Dallas

Accredited

ABSTRACT

This paper introduces an approach for analyzing multivariate spatial cluster/outlier in local scale. Even though spatial cluster/outlier has various definitions, the fundamental of spatial cluster/outlier is based on spatial association. Existing methods for measuring local spatial association had a limitation of applying multiple numbers of variables. Univariate local spatial association measures such as local Moran’s Ii, local Geary’s Ci and Getis and Ord’s Gi * are widely used, and bivariate local spatial association measures are already developed; Cross Moran and Lee’s Li. However, the measures are not used for measuring spatial association among three or more variables. This is a critical limitation when spatial variation with the complex multi-dimensional approaches is explained and described. The measure in this paper, multivariate local spatial association measure, is based on Mahalanobis Distance (MD) and it enables distinguishing spatial similarities and differences among multiple numbers of data sets simultaneously. MD considers variables’ means, variances and co-variances and allows measuring the variables’distribution. It is the same concept as distance measuring with Euclidean Distance but improved. Significance of MD could be tested because it is following chi-square distribution when the variables are multi-normal. Local MD is applied to demographic variables, in- and out-migration in Seoul Metropolitan Area. The spatial variation of multivariables could be identified by chi-squared p-value map, and a local MD map is provided to show the detected spatial clusters or outliers at a given significance level.

Citation status

* References for papers published after 2022 are currently being built.