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Categories and Quantities

  • John C. Gower

Summary

The rank of a matrix of categorical variables is defined. This may be used as a basis of multivariate methods for approximating categorical data in a similar way that the rank of a quantitative data matrix may be used to define standard methods such as multidimensional scaling, multiple correspondence analysis, principal components analysis and non-linear principal components analysis. Several problems are outlined that depend on the notion of categorical rank. The algorithmic tools for handling categorical rank need to be developed.

Keywords

Multidimensional Scaling Correct Prediction Neighbour Region Multiple Correspondence Analysis Prediction Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Eckart, C. and Young, G. (1936) the approximation of one matrix by another of lower rank. Psychometrika. 1, 211 - 218.Google Scholar
  2. Gifi, A.A.(1990). Nonlinear Multivariate Analysis. Chichester: John Wiley and Sons, 579 + xx pp.Google Scholar
  3. Gower J. C. (1993). The construction of neighbour-regions in two dimensions for prediction with multi-level categorical variables. In: Information and Classication: Concepts - Methods - Applications Proceedings 16th Annual Conference of the Gesellschaft fur Klassifikation, Dortmund, April 1992 Eds. O. Opitz, B. Lausen and R. Klar. Springer Verlag: Heidelberg - Berlin, 174 - 189.Google Scholar
  4. Gower, J.C. and Hand, D. J. (1996). Biplots. London: Chapman and Hall, 277 + xvi pp.Google Scholar
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  6. Gower, J.C., Meulman, J. J., and Arnold, G. M. (1999). Non-metric linear biplots. Journal of Classification,16, 181-196. Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • John C. Gower
    • 1
  1. 1.Department of StatisticsThe Open UniversityMilton KeynesUK

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