Phenomena with a constrained sample space appear frequently in practice. This is the case, for example, with strictly positive data, or with compositional data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real sp...

The amalgamation operation is frequently used to reduce the number of parts of compositional data but it is a non-linear operation in the simplex with the usual geometry, the Aitchison geometry. The concept of balances between groups, a particular coordinate system designed over binary partitions of the parts, could be an alternative to the amalgamation in some cases. In this work we discuss th...

data Peter Filzmoser, Karel Hron, Clemens Reimann Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria. Tel +43 1 58801 10733, FAX +43 1 58801 10799 Department of Mathematical Analysis and Applications of Mathematics, Palacký University, Faculty of Science, 17. listopadu 12, CZ-77146 Olomouc, Czech Republic Geological...

the closed nature of geochemical data has been proven in many studies. compositional data have special properties that mean that standard statistical methods cannot be used to analyse them. these data imply a particular geometry called aitchison geometry in the simplex space. for analysis, the dataset must first be opened by the various transformations provided. one of the most popular of the a...

Compositional data need a special treatment prior to correlation analysis. In this paper we argue why standard transformations for compositional data are not suitable for computing correlations, and why the use of raw or log-transformed data is neither meaningful. As a solution, a procedure based on balances is outlined, leading to sensible correlation measures. The construction of the balances...

Compositional data are nonnegative carrying relative, rather than absolute, information—these often with a constant-sum constraint on the sample values, for example, proportions or percentages summing to 1% 100%, respectively. Ratios between components of composition important since they unaffected by particular set chosen. Logarithms ratios (logratios) fundamental transformation in ratio appro...

Multivariate outlier detection is usually based on Mahalanobis distances, by plugging in robust estimates of location and covariance. For compositional data, carrying only relative information, a special transformation needs to be consulted in order to be able to work in the appropriate geometry. The effect of the transformation is discussed in this contribution. Furthermore, different possibil...