Fisher discriminant method for multiple compositional-data variables in simplex space
-
摘要: 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.
-
关键词:
- 单形空间 /
- 成分数据 /
- Fisher判别分析
Abstract: 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.-
Key words:
- simplex space /
- compositional data /
- Fisher discriminant analysis
-
[1] Aitchison J.The statistical analysis of compositional data[M].London:London Chapman and Hall,1986 [2] Filzmoser P,Hron K.Outlier detection for compositional data using robust methods[J].Mathematical Geoscience,2008,40:233-248. [3] Kovacs L O,Kovacs G P,Martin-Fernandez J A,et al.Major-oxide compositional discrimination in Cenozoic volcanites of Hungary[C]//Buccianti A,Mateu-Figueras G,Pawlowsky-Glahn V.Compositional data analysis in the geosciences:from theory to practice.London:Geological Society,2006:11-23 [4] Filzmoser P,Hron K,Templ M.Discriminant analysis for compositional data and robust parameter estimation[J].Computation Statistics,2012,27:585-604 [5] 郭丽娟.多元成分数据的若干分析方法研究[D].北京:北京航空航天大学经济管理学院,2011 Guo Lijuan.Methods of Multivariate analysis on compositional data[D].Beijing:School of Economics and Management,Beijing University of Aeronawtics and Astoonantics,2011(in Chinese) [6] Aitchison J,Egozcue J J.Compositional data analysis:where are we and where should we be heading [J].Mathematical Geology,2005,37(7):829-850 [7] Palarea-Albaladeio J,Martin-Fernandez J A,Soto J A.Dealing with distances and transformations for fuzzy C-means clustering of compositional data[J].Journal of Classification,2012:29:144-169 [8] Aitchison J.The one-hour course in compositional data analysis or compositional data analysis is simple[C]//Proceedings of IAMG'97-The 1997 Annual Conference of the International Association for Mathematical Geology.Barcelona:CIMNE,1997:3-35 [9] Martin-Fernandez J A,Barcelo-vidal C,Pawlowsky-Glahn V.A critical approach to non-parametric classification of compositional data[C]//Rizzi A,Vichi M,Bock H H.Advances in data science and classification.Berlin:Springer,1998:49-56 [10] Pawlowsky-Glahn V,Buccianti A.Compositional data analysis-theory and applications[M].Chichester:John Wiley & Sons,2011 [11] 周蒂,张光前,王仁铎,等.成分数据的统计分析[M].北京:中国地质大学出版社,1990 Zhou Di,Zhang Guangqian,Wang Renduo,et al.The statistical analysis of compositional data[M].Beijing:Press of China University of Geosciences,1990(in Chinese) -
点击查看大图
计量
- 文章访问数: 1809
- HTML全文浏览量: 193
- PDF下载量: 797
- 被引次数: 0
下载:
