Discriminant analysis for compositional data and robust parameter estimation

作者：Filzmoser Peter^*; Hron Karel; Templ Matthias

来源：Computational Statistics, 2012, 27(4): 585-604.

DOI：10.1007/s00180-011-0279-8

• Compositional data
• Logratio transformations
• Discriminant analysis
• Robustness

Compositional data, i.e. data including only relative information, need to be transformed prior to applying the standard discriminant analysis methods that are designed for the Euclidean space. Here it is investigated for linear, quadratic, and Fisher discriminant analysis, which of the transformations lead to invariance of the resulting discriminant rules. Moreover, it is shown that for robust parameter estimation not only an appropriate transformation, but also affine equivariant estimators of location and covariance are needed. An example and simulated data demonstrate the effects of working in an inappropriate space for discriminant analysis.

• 出版日期2012-12