Principal component analysis for compositional data with outliers

  • Filzmoser P
  • Hron K
  • Reimann C
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Abstract

For compositional data a special transformation is needed prior to applying multivariate data analysis tools. If this is not done, the correlation structure can be completely biased and results become useless. If robust multivariate techniques like principal component analysis (PCA) are used, the transformed data need to have full rank, and thus a transformation like the centered logratio transformation can not be used. In this paper we use the isometric logratio transformation for robust PCA. However, this transformation has the disadvantage that the new variables are not directly interpretable. Here it is shown how the resulting robust scores and loadings can be back-transformed. Using a real data set we demonstrate the difference of the results when not taking appropriate transformations and when applying classical or robust PCA.

Author-supplied keywords

  • compositional data
  • isometric logratio transformation
  • prin- cipal component analysis
  • robust statistics

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Authors

  • P Filzmoser

  • K Hron

  • C Reimann

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