Multivariate Spatial Cluster Analysis Using Mahalanobis Distance (마할라노비스 거리를 이용한 다변량 공간 클러스터 분석)

Monghyeon Lee (이몽현)

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.

KEYWORDS

Mahalanobis Distance, Spatial cluster, Multivariate local spatial association measure

Citation status

* References for papers published after 2023 are currently being built.

[book] Aldstadt, J. / 2010 / Spatial clustering, In Handbook of Applied Spatial Analysis / Springer : 279~300

[journal] Anselin, L. / 1995 / Local indicators of spatial association- LISA / Geographical Analysis 27 : 93~115

[book] Anselin, L. / 1996 / The Moran scatterplot as an ESDA tool to assess local intability in spatial association, In Spatial Analytical Perspectives in GIS / Taylor & Francis : 111~125

[confproc] Anselin, L. / 2002 / Visualizing multivariate spatial correlation with dynamically linked windows / New Tools for Spatial Data Analysis: Proceedings of the Specialist Meeting : 51~

[journal] Clark, J.D. / 1993 / A multivariate model of female black bear habitat use for a geographic information system / The Journal of Wildlife Management 57(3) : 519~526

[book] Cliff, A.D. / 1973 / Spatial Autocorrelation / Pion

[journal] Demattei, C. / 2006 / Arbitrarily shaped multiple spatial cluster detection for case event data / Computational Statistics & Data Analysis 51(8) : 3931~3945

[journal] De Maesschalck, R. / 2000 / The MD / Chemometrics and Intelligent Laboratory Systems 50(1) : 1~18

[journal] Geary, R.C. / 1954 / The contiguity ratio and statistical mapping / Incorporated Statistician 5 : 115~145

[journal] Getis, A. / 1992 / The analysis of spatial association by distance statistics / Geographical Analysis 24 : 189~206

[journal] Ord, J. / 1995 / Local spatial autocorrelation statistics: distributional issues and an application / Geographical Analysis 27(4) : 286~306

[confproc] Guo, D. / 2002 / Opening the black box: interactive hierarchical clustering for multivariate spatial patterns / Association for Computing Machinery: the 10th ACM international symposium on Advances in geographic information systems : 131~136

[journal] 황효정 / 2008 / Application of Bivariate Spatial Association for the Quantitative Marine Environment Pattern Analysis / 한국지리정보학회지 / 한국지리정보학회 11(1) : 155~166

[book] Jacquez, G. / 2008 / Spatial cluster analysis, In The Handbook of Geographical Information Science / Blackwell Publishing : 395~416

[journal] Kelsall, J.E. / 1995 / Non-parametric estimation of spatial variation in relative risk / Statistics in Medicine 14 : 2335~2342

[journal] Knick, S. / 1997 / Distribution of black-tailed jackrabbit habitat determined by GIS in southwestern Idaho / The Journal of Wildlife Management 61(1) : 75~85

[journal] Knick, S. / 1998 / Limitations to mapping habitat use areas in changing landscapes using the MD statistic / Journal of Agricultural, Biological, and Environmental Statistics 3 : 311~322

[journal] Krzanowski, W. / 1988 / A criterion for determining the number of groups in a data set using sum-of-squares clustering / Biometrics 44 : 23~34

[journal] Kulldorff, M. / 1997 / A spatial scan statistic / Communications in Statistics- Theory and Methods 26(6) : 1481~1496

[journal] Lee, S.-I. / 2001 / Developing a bivariate spatial association measure: an integration of Pearson’s r and Moran’s I / Journal of Geographical Systems 3 : 36~385

[thesis] Lee, S.-I. / 2001 / Spatial Association Measures for an ESDA-GIS Framework: Developments, Significance Tests, and Applications to Spatio-Temporal Income Dynamics of U.S. Labor Market Areas, 1969-1999 / 박사 / The Ohio State University

[journal] Lee, S.-I. / 2001 / A spatial statistical approach to migration studies / Journal of the Korean Association of Regional Geographers 7(3) : 107~120

[journal] 이상일 / 2010 / A GIS-Based Method for Delineating Spatial Clusters: A Modified AMOEBA Technique / 대한지리학회지 / 대한지리학회 45(4) : 502~520

[confproc] Lu, C.T. / 2003 / Detecting spatial outliers with multiple attributes / IEEE International Conference on Tools with Artificial Intelligence 15 : 122~128

[journal] Miller, H. / 2004 / Tobler's first law and spatial analysis / Annals of the Association of American Geographers 94(2) : 284~289

[journal] Moran, P.A.P. / 1948 / The interpretation of statistical maps / Journal of the Royal Statistical Society Series B 10 : 243~251

[journal] Penny, K.I. / 1996 / Appropriate critical values when testing for a single multivariate outlier by using the MD / Journal of the Royal Statistical Society Series C 45(1) : 73~81

[journal] Plane, D. / 1981 / Estimation of place-to-place migration flows from net migration totals: a minimum information approach / International Regional Science Review 6 : 33~51

[book] Plane, D. / 1994 / The Geographical Analysis of Population: With Applications to Planning and Business / John Wiley & Sons

[journal] Ripley, B.D. / 1977 / Modeling spatial patterns (with discussion) / Journal of the Royal Statistical Society Series B 39 : 172~212

[journal] Shenk, J. / 1991 / Population definition, sample selection, and calibration procedures for near-ingrared reflectance spectroscope / Crop Science 31 : 469~474

[confproc] Szalay, A.S. / 2002 / Spatial clustering of galaxies in large datasets / SIPE Astronomy Telescopes and Instruments 4847(1) : 22~28

[journal] Vinson, T. / 1999 / The spatial clustering of child maltreatment: are micro-social environments involved? / Australian Institute of Criminology 119 : 1~6

[journal] Wartenberg, D. / 1985 / Multivariate spatial correlation: a method for exploratory geographical analysis / Geographical Analysis 17 : 263~283

[journal] Wheeler, D. / 2007 / A comparison of spatial clustering and cluster detection techniques for childhood leukemia incidence in Ohio, 1996–2003 / International Journal of Health Geographics 6(13) : 1~16

[journal] Woodall, W.G. / 2003 / A review and analysis of the Mahalanobis-Taguchi system / Technometrics 45(1) : 1~15

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