Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and co...

In this article we present a novel kernel function, logRatio, which was designed to address two common problems in biological applications: data preprocessing and attribute interaction modelling. An extension of the SVMRFE feature selection algorithm was built around this new kernel function and compared with the original on a number of biological data and text classification problems. Experime...

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional coherence, which assures that results are invariant to considering subsets of the composition. The second ...

Abstract. Many practical data sets in environmental sciences, official statistics and various other disciplines are in fact compositional data because only the ratios between the variables are informative. Compositional data are represented in the Aitchison geometry on the simplex, and for applying statistical methods designed for the Euclidean geometry they need to be transformed first. The is...

Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or a...

Measuring the rate of return is an important issue for theory and practice of investments in the stock market. A common measure for rate of return is the logarithm of the ratio of successive prices (LogRatio). In this paper it is shown that LogRatio as well as arithmetic return rate (Ratio) have several disadvantages. As an alternative relative differences (RelDiff) are proposed to measure retu...

The logratio transformation (Aitchison, 1981, 1986) opened the way to statistically rigorous analysis of compositional data. Most statistical problems in compositional data analysis can be formulated in terms of logratios, and solved accordingly. However, some problems are more easily described and solved in terms of raw compositional variables. Raw compositions with k components are restricted...

This definition of the unit simplex differs subtly from that of Aitchison (1982), as we relax the condition that the components of u must be strictly positive. Under this scenario, use of the ratio (or logratio) to compare different compositions is not ideal since it is undefined in some instances, and subcompositional analysis is also not appropriate due to the possibility of division by zero....

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done like in usual ...