Logcontrast PLS discriminant model of compositional data

Abstract

This paper studies discriminant modeling method of compositional data. The logcontrast PLS discriminant model of compositional data is proposed by adopting centered logratio transformation of compositional data and then implementing partial least squares (PLS) discriminant method to the transformed data. The model presents the following advantages: i) the transformed variable is symmetrical to the components of the original compositional data, which is favorable in explaining the modeling results; ii) PLS related methods, without strict statistical distribution assumption to the data, are typically adaptive to the compositional data notable for its unit sum constraint and complex distribution; iii) the modeling process and computation are straightforward; iv) conforming to the basic algebraic theories of compositional data, the obtained discriminant function is formally proved satisfying the logcontrast property. Finally, to evaluate this method, two experiments with simulated and real compositional data sets were performed respectively, which illustrate the validity and practicability of the model.