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Unclassed matrix shading and optimal ordering in hierarchical cluster analysis

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Abstract

A method is presented for the graphic display of proximity matrices as a complement to the common data analysis techniques of hierarchical clustering. The procedure involves the use of computer generated shaded matrices based on unclassed choropleth mapping in conjunction with a strategy for matrix reorganization. The latter incorporates a combination of techniques for seriation and the ordering of binary trees.

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References

  • CARMICHAEL, J.W., and SNEATH, P.H.A. (1969), “Taxometric Maps,”Systematic Zoology, 18, 402–415.

    Google Scholar 

  • CHANG, K. (1978), “Visual Aspects of Class Intervals in Choroplethic Mapping,”Cartographic Journal, 15, 42–48.

    Google Scholar 

  • DEGERMAN, R. (1982), “Ordered Binary Trees Constructed Through an Application of Kendall's Tau.”Psychometrika, 47, 523–527.

    Google Scholar 

  • DIXON, W.J., ed. (1983),BMDP Statistical Software, Berkeley: University of California Press.

    Google Scholar 

  • GALE, N., and HALPERIN, W.C. (1982), “A Case for Better Graphics: The Unclassed Choropleth Map,”The American Statistician, 36, 330–336.

    Google Scholar 

  • GRUVAEUS, G., and WAINER, H. (1972), “Two Additions to Hierarchical Cluster Analysis,”British Journal of Mathematical and Statistical Psychology, 25, 200–206.

    Google Scholar 

  • HARTIGAN, J.A. (1975),Clustering Algorithms, New York: John Wiley.

    Google Scholar 

  • HUBERT, L.J., GOLLEDGE, R.G., and RICHARDSON, G.D. (1982), “Proximity Matrix Reorganization and Hierarchical Clustering,”Environment and Planning A, 14, 195–203.

    Google Scholar 

  • JENKS, G.F., and CASPELL, F.C. (1971), “Error on Choroplethic Maps: Definition, Measurement, Reduction,”Annals of the Association of American Geographers, 61, 217–244.

    Google Scholar 

  • JENKS, G.F., and COULSON, M.R. (1963), “Class Intervals for Statistical Maps,”International Yearbook of Cartography, 3, 113–119.

    Google Scholar 

  • KENDALL, D.G. (1971), “Seriation from Abundance Matrices,” inMathematics in the Archaeological and Historical Sciences, eds. F.R. Hodson, D.G. Kendall, and P. Tautu, Edinburgh: Edinburgh University Press, 215–252.

    Google Scholar 

  • KENDALL, M.G. (1970),Rank Correlation Methods, London: Griffin.

    Google Scholar 

  • LING, R.F. (1973), “A Computer Generated Aid for Cluster Analysis,”Communications of the ACM, 16, 355–361.

    Google Scholar 

  • McCAMMON, R.B., and WENNINGER, G. (1970), “The Dendrograph,” Computer Contrib., No. 48, University of Kansas, Kansas Geological Survey.

  • MACKAY, J.R. (1955), “An Analysis of Isopleth and Choropleth Class Intervals,”Economic Geography, 31, 71–81.

    Google Scholar 

  • MONMONIER, M.S. (1975), “Class Intervals to Enhance the Visual Correlation of Choropleth Maps,”Canadian Cartographer, 12, 161–178.

    Google Scholar 

  • MONMONIER, M.S. (1976), “Modifying Objective Functions and Constraints for Maximizing Visual Correspondence of Choropleth Maps,”Canadian Cartographer, 13, 21–34.

    Google Scholar 

  • MULLER, J.C. (1976), “Number of Classes and Choropleth Pattern Characteristics,”American Cartographer, 3, 169–175.

    Google Scholar 

  • ROBINSON, A., SALE, R., and MORRISON, J. (1978),Elements of Cartography, New York: John Wiley.

    Google Scholar 

  • ROBINSON, W.S. (1951), “A Method for Chronologically Ordering Archaeological Deposits,”American Antiquity, 16, 293–301.

    Google Scholar 

  • SNEATH, P.H.A. (1957), “The Application of Computers to Taxonomy,”Journal of General Microbiology, 17, 201–226.

    PubMed  Google Scholar 

  • SNEATH, P.H.A. and SOKAL, R.R. (1973),Numerical Taxonomy, San Francisco: W.H. Freeman.

    Google Scholar 

  • SOKAL, R.R., and SNEATH, P.H.A. (1963),Principles of Numerical Taxonomy, San Francisco: W.H. Freeman.

    Google Scholar 

  • TOBLER, W.R. (1973), “Choropleth Maps Without Class Intervals?”Geographical Analysis, 3, 262–265.

    Google Scholar 

  • TOMLINSON, R.F., ed. (1970),Environmental Information Systems, Ottawa: International Geographical Union Commission on Geographical Data Sensing and Processing.

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Partial support for this research was provided by NIJ Grant #82-IJ-CX-0019 and NSF Grant #SES82-06067. The authors wish to acknowledge the assistance of Professors L.J. Hubert, R.G. Golledge, and W.R. Tobler.

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Gale, N., Halperin, W.C. & Costanzo, C.M. Unclassed matrix shading and optimal ordering in hierarchical cluster analysis. Journal of Classification 1, 75–92 (1984). https://doi.org/10.1007/BF01890117

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