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Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Daunis i Estadella, Josep
ThiÃ³ i FernÃ¡ndez de Henestrosa, Santiago Mateu i Figueras, GlÃ²ria 

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  
http://hdl.handle.net/2072/273441  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
AnÃ lisi multivariable  Congressos
Multivariate analysis  Congresses EstadÃstica matemÃ tica  Congressos Mathematical statistics  Congresses CorrelaciÃ³ (EstadÃstica)  Congressos Correlation (Statistics)  Congresses 

Two More Things about Compositional Biplots: Quality of Projection and Inclusion of Supplementary Elements  
info:eurepo/semantics/conferenceObject  
Recercat 