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Biplots of fuzzy coded data

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Abstract
A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.

Suggested Citation

  • Zerrin Asan & Michael Greenacre, 2008. "Biplots of fuzzy coded data," Economics Working Papers 1077, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1077
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    File URL: https://econ-papers.upf.edu/papers/1077.pdf
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    Cited by:

    1. Michael Greenacre, 2012. "Fuzzy coding in constrained ordinations," Economics Working Papers 1325, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Michael Greenacre, 2014. "Size and shape in the measurement of multivariate proximity," Economics Working Papers 1444, Department of Economics and Business, Universitat Pompeu Fabra.

    More about this item

    Keywords

    defuzzification; fuzzy coding; indicator matrix; measure of fit; multivariate data; multiple correspondence analysis; principal component analysis.;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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