Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Comparison of Methods for Reducing the Dimension of Compositional Data with Zero Values

  • Received : 2012.05.02
  • Accepted : 2012.06.16
  • Published : 2012.07.31
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Abstract

Compositional data consist of compositions that are non-negative vectors of proportions with the unit-sum constraint. In disciplines such as petrology and archaeometry, it is fundamental to statistically analyze this type of data. Aitchison (1983) introduced a log-contrast principal component analysis that involves logratio transformed data, as a dimension-reduction technique to understand and interpret the structure of compositional data. However, the analysis is not usable when zero values are present in the data. In this paper, we introduce 4 possible methods to reduce the dimension of compositional data with zero values. Two real data sets are analyzed using the methods and the obtained results are compared.

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References

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