Ítem


Two More Things about Compositional Biplots: Quality of Projection and Inclusion of Supplementary Elements

The biplot is a widely and powerful methodology used with multidimensional data sets todescribe and display the relationships between observations and variables in an easy way.Compositional data consist of positive vectors each of which is constrained to have a constant sum;due to this property standard biplots can not be performed with compositional data, instead of aprevious transformation of the data is performed. Due to this constant sum constraint, atransformation of data is needed before performing a biplot and, consequently, special interpretationrules are required. However, these rules can only be safely applied when the elements of a biplothave a good quality of projection, for which a new measure is introduced in this paper. Also, weextend the compositional biplot defined by Aitchison and Greenacre on 2002, in order to includethe display supplementary elements that are not used in the definition of the compositional biplot.Different types of supplementary elements are considered: supplementary parts of the composition,supplementary continuous variables external to the composition, supplementary categoricalvariables and supplementary observations. The projection of supplementary parts of thecomposition is done by means of the equivalence of clr and lr biplots. The other supplementaryprojections are done by classical methodology. Both the qualities of projections and thesupplementary projections are explained using real geological data: a sample of 72 observations ofsoil in an area about 20 km west of Kiev in the area south of Kiev Polessie

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Altres contribucions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Autor: Daunis i Estadella, Josep
Thió i Fernández de Henestrosa, Santiago
Mateu i Figueras, Glòria
Resum: The biplot is a widely and powerful methodology used with multidimensional data sets todescribe and display the relationships between observations and variables in an easy way.Compositional data consist of positive vectors each of which is constrained to have a constant sum;due to this property standard biplots can not be performed with compositional data, instead of aprevious transformation of the data is performed. Due to this constant sum constraint, atransformation of data is needed before performing a biplot and, consequently, special interpretationrules are required. However, these rules can only be safely applied when the elements of a biplothave a good quality of projection, for which a new measure is introduced in this paper. Also, weextend the compositional biplot defined by Aitchison and Greenacre on 2002, in order to includethe display supplementary elements that are not used in the definition of the compositional biplot.Different types of supplementary elements are considered: supplementary parts of the composition,supplementary continuous variables external to the composition, supplementary categoricalvariables and supplementary observations. The projection of supplementary parts of thecomposition is done by means of the equivalence of clr and lr biplots. The other supplementaryprojections are done by classical methodology. Both the qualities of projections and thesupplementary projections are explained using real geological data: a sample of 72 observations ofsoil in an area about 20 km west of Kiev in the area south of Kiev Polessie
Accés al document: http://hdl.handle.net/2072/273441
Llenguatge: eng
Editor: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Drets: Tots els drets reservats
Matèria: Anàlisi multivariable -- Congressos
Multivariate analysis -- Congresses
Estadística matemàtica -- Congressos
Mathematical statistics -- Congresses
Correlació (Estadística) -- Congressos
Correlation (Statistics) -- Congresses
Títol: Two More Things about Compositional Biplots: Quality of Projection and Inclusion of Supplementary Elements
Tipus: info:eu-repo/semantics/conferenceObject
Repositori: Recercat

Matèries

Autors