Correlation Coefficient of Compositional Data Based on Isometric Logratio Transformation

Compositional data is a relatively independent field in statistical analysis. Aitchison used to introduce the additive-logratio transformation (alr) and centered logratio transformation (clr) in 1986, which are effective tools to solve the problem of compositional data. But those approaches are not isometry ways, and the interpretation of transformed data might be different from the expected properties. Then Egozcue put forward the isometric logratio transformation, which can transform the simplex space into the real Euclidean space. This paper aims at introducing a new approach to calculate the correlation of two sets of compositional data. This approach based on the isometric logratio transformation can preserve all metric properties and solve the problem of calculation of correlation coefficient on compositional data.