Fisher discriminant analysis of compositional data

This paper studies discriminant modeling method of compositional data. By adopting logratio transformation of compositional data and then implementing Fisher discriminant modeling method to the transformed data, the logcontrast linear discriminant function of compositional data is derived. The model presents the following advantages: i) the transformed data, which is scaled up to a broader range of (-∞,+∞), releases the (0,1) bound and unit sum constraints of the compositional data; ii) the modeling and computational processes to the transformed data are more feasible and straightforward; iii) the derived linear discriminant function presents a form of logcontrast combination of the original data, satisfying the basic algebraic theories of compositional data. To evaluate the presented method, two experiments with simulated and real compositional data sets were performed respectively, which illustrate the validity and practicability of the model.