Fisher discriminant method for multiple compositional-data variables in simplex space

As foundation work, the algebra operations of compositional-data vector were investigated, based on the algorithms of compositional data in simplex space. Further, according to traditional method, Fisher discriminant analysis (FDA) on multiple compositional-data variables was proposed. The novel method built the linear discriminant function based on the operations of compositional-data vectors. And the discriminant rule on compositional-data variables was investigated with the theory of distance discriminant analysis. The sample can be classified according to the distances between the projective point of a sample for discrimination and that of the cluster centers. Both simulation results and application analysis show the usefulness of the proposed methods. The algebra system of compositional-data vectors lays the foundation for extending the other multivariate statistical method to multiple compositional-data variables.