Zero Replacement in Compositional Data Sets

  • J. A. Martín-Fernández
  • C. Barceló-Vidal
  • V. Pawlowsky-Glahn
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The sample space of compositional data is the open simplex. Therefore, zeros in a compositional data set are identified 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 hierarchical cluster analysis of compositional data.


Hierarchical Cluster Analysis Imputation Method Compositional Data Mathematical Geology Vector Space Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • J. A. Martín-Fernández
    • 1
  • C. Barceló-Vidal
    • 1
  • V. Pawlowsky-Glahn
    • 2
  1. 1.Dept. Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain
  2. 2.Dept. Matemàtica Aplicada III, ETSECCPBUniversitat Politècnica de CatalunyaBarcelonaSpain

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