robCompositions (version 1.9.1)

daFisher: Discriminant analysis by Fisher Rule.

Description

Discriminant analysis by Fishers rule.

Usage

daFisher(x, grp, coda = TRUE, method = "classical", plotScore=FALSE)

Arguments

x

a matrix or data frame containing the explanatory variables (training set)

grp

grouping variable: a factor specifying the class for each observation.

coda

TRUE, when the underlying data are compositions.

method

classical or robust

plotScore

TRUE, if the scores should be plotted automatically.

Value

• an object of class daFisher including the following elements
• B
  Between variance of the groups
• W
  Within variance of the groups
• loadings
  loadings
• coda
  coda

Details

The Fisher rule leads only to linear boundaries. However, this method allows for dimension reduction and thus for a better visualization of the separation boundaries. For the Fisher discriminant rule (Fisher, 1938; Rao, 1948) the assumption of normal distribution of the groups is not explicitly required, although the method looses its optimality in case of deviations from normality.

The classical Fisher discriminant rule is invariant to ilr and clr transformations. The robust rule is invariant to ilr transformations if affine equivariant robust estimators of location and covariance are taken.

Robustification is done (method robust) by estimating the columnwise means and the covariance by the Minimum Covariance Estimator.

References

Filzmoser, P. and Hron, K. and Templ, M. (2009) Discriminant analysis for compositional data and robust parameter estimation. Research Report SM-2009-3, Vienna University of Technology, 27 pages.

Fisher, R. A. (1938) The statistical utiliziation of multiple measurements. Annals of Eugenics, 8:376-386.

Rao, C.R. (1948) The utilization of multiple measurements in problems of biological classification. Journal of the Royal Statistical Society, Series B, 10:159-203.

See Also

Linda

Examples

require(MASS)
x1 <- mvrnorm(20,c(0,0,0),diag(3))
x2 <- mvrnorm(30,c(3,0,0),diag(3))
x3 <- mvrnorm(40,c(0,3,0),diag(3))
X <- rbind(x1,x2,x3)
grp=c(rep(1,20),rep(2,30),rep(3,40))

#par(mfrow=c(1,2))
d1 <- daFisher(X,grp=grp,method="classical",coda=FALSE)
d2 <- daFisher(X,grp=grp,method="robust",coda=FALSE)
d2