单形空间中多元成分数据的Fisher判别方法

首先,基于Aitchison单形空间成分数据运算法则,提出成分数据向量的代数体系,其中包括成分数据向量的加法、数乘、减法、内积、范数以及距离等定义.在此基础上,根据Fisher判别分析原理,建立多元成分数据的线性判别函数,以及利用距离判别的思想,根据待判样本投影点的得分与各类中心投影点的均值之间的距离,对待判样本进行归类建立判别规则,从而提出一种针对多元成分数据的判别方法.最后,通过仿真方法及实际案例验证该方法的有效性.给出的成分数据向量的代数体系为将其他多元统计方法推广到多元成分数据奠定了基础.

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.