Between-class Principal Component Analysis

Between-class Principal Component Analysis

bcPCA(data, class, row.w = NULL, scale.unit = TRUE, ncp = 5)

Arguments

data

data frame with only numeric variables

class

factor specifying the class

row.w

numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used.

scale.unit

logical. If TRUE (default) then data are scaled to unit variance.

ncp

number of dimensions kept in the results (by default 5)

Details

Between-class Principal Component Analysis consists in two steps : 1. Computation of the barycenter of data rows for each category of class 2. Principal Component Analysis of the set of barycenters

It is a quite similar to Linear Discriminant Analysis, but the metric is different.

It can be seen as a special case of PCA with instrumental variables, with only one categorical instrumental variable.

Value

An object of class PCA from FactoMineR package, with the original data as supplementary individuals, and an additional item :

ratio

the between-class inertia percentage

References

Bry X., 1996, Analyses factorielles multiples, Economica.

Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)

Author

Nicolas Robette

See also

PCAiv, DA

Examples

library(FactoMineR)
data(decathlon)
points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4"))
res <- bcPCA(decathlon[,1:10], points)
# categories of class
plot(res, choix = "ind", invisible = "ind.sup")

# variables in decathlon data
plot(res, choix = "var")

# between-class inertia percentage
res$ratio
#> [1] 0.2673959