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DaunisiEstadella, Pepus
ThiÃ³ i FernÃ¡ndez de Henestrosa, Santiago Mateu i Figueras, GlÃ²ria 

2011 May 11  
The biplot is a widely and powerful methodology used with multidimensional data sets to describe 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 a previous transformation of the data is performed. Due to this constant sum constraint, a transformation of data is needed before performing a biplot and, consequently, special interpretation rules are required. However, these rules can only be safely applied when the elements of a biplot have a good quality of projection, for which a new measure is introduced in this paper. Also, we extend the compositional biplot defined by Aitchison and Greenacre on 2002, in order to include the 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 categorical variables and supplementary observations. The projection of supplementary parts of the composition is done by means of the equivalence of clr and lr biplots. The other supplementary projections are done by classical methodology. Both the qualities of projections and the supplementary projections are explained using real geological data: a sample of 72 observations of soil in an area about 20 km west of Kiev in the area south of Kiev Polessie  
application/pdf  
http://hdl.handle.net/10256/13607  
eng  
Universitat PolitÃ¨cnica de Catalunya. Centre Internacional de MÃ¨todes NumÃ¨rics en Enginyeria (CIMNE)  
info:eurepo/semantics/altIdentifier/isbn/9788487867767  
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/bookPart  
DUGiDocs 