sym.interval.pca: Interval Principal Components Analysis

Description

Cazes, Chouakria, Diday and Schektman (1997) proposed the Centers and the Tops Methods to extend the well known principal components analysis method to a particular kind of symbolic objects characterized by multi--values variables of interval type.

Usage

sym.interval.pca(sym.data, method = c("classic", "tops", "centers"))

Arguments

sym.data

Shoud be a symbolic data table read with the function read.sym.table(...)

method

It is use so select the method, "classic" execute a classical principal component analysis over the centers of the intervals, "tops" to use the vertices algorithm and "centers" to use the centers algorithm.

Value

Sym.Components: This a symbolic data table with the interval principal components. As this is a symbolic data table we can apply over this table any other symbolic data analysis method (symbolic propagation).
Sym.Prin.Correlations: This is the interval correlations between the original interval variables and the interval principal components, it can be use to plot the symbolic circle of correlations.

References

Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.

Cazes P., Chouakria A., Diday E. et Schektman Y. (1997). Extension de l'analyse en composantes principales a des donnees de type intervalle, Rev. Statistique Appliquee, Vol. XLV Num. 3 pag. 5-24, France.

Chouakria A. (1998) Extension des methodes d'analysis factorialle a des donnees de type intervalle, Ph.D. Thesis, Paris IX Dauphine University.

Makosso-Kallyth S. and Diday E. (2012). Adaptation of interval PCA to symbolic histogram variables, Advances in Data Analysis and Classification July, Volume 6, Issue 2, pp 147-159.

Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.

Examples

Run this code

data(oils)  
res<-sym.interval.pca(oils,'centers')
sym.scatterplot(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                labels=TRUE,col='red',main='PCA Oils Data')
sym.scatterplot3d(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                  sym.var(res$Sym.Components,3),color='blue',main='PCA Oils Data')
sym.scatterplot.ggplot(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                       labels=TRUE)
sym.circle.plot(res$Sym.Prin.Correlations)

res<-sym.interval.pca(oils,'classic')
plot.PCA(res,choix="ind")
plot.PCA(res,choix="var")

data(lynne2)
res<-sym.interval.pca(lynne2,'centers')
sym.scatterplot(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                labels=TRUE,col='red',main='PCA Lynne Data')
sym.scatterplot3d(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                  sym.var(res$Sym.Components,3),color='blue', main='PCA Lynne Data')
sym.scatterplot.ggplot(sym.var(res$Sym.Components,1),sym.var(res$Sym.Components,2),
                       labels=TRUE)
sym.circle.plot(res$Sym.Prin.Correlations)

data(StudentsGrades)
st<-StudentsGrades
s.pca<-sym.interval.pca(st)
plot.PCA(s.pca,choix="ind")
plot.PCA(s.pca,choix="var")