Zero Replacement in Compositional Data Sets

Abstract

The sample space of compositional data is the open simplex. Therefore, zeros in a compositional data set are indentified either with below detection limit values, or lead to a division of the data set into different subpopulations with the corresponding lower dimensional sample space. Most multivariate data analysis techniques require complete data matrices, thus calling for a strategy of imputation of zeros in the first case. Existing replacement methods of rounded zeros are reviewed, and a new method is proposed, who's properties are analyzed and illustrated. The method is applied in a hierchical cluster analysis of compositional data.