Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada
Daunis i Estadella, Josep
Thió i Fernández de Henestrosa, Santiago
Mateu i Figueras, Glòria
2017-02-15T11:30:11Z
2017-02-15T11:30:11Z
2011-05-11
http://hdl.handle.net/10256/13607
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
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Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
CoDaWork 2011. The 4th International Workshop on Compositional Data Analysis
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Two More Things about Compositional Biplots: Quality of Projection and Inclusion of Supplementary Elements
info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/openAccess