daFisher: Discriminant analysis by Fisher Rule.

In robCompositions: Compositional Data Analysis

Discriminant analysis by Fisher Rule.

Description

Discriminant analysis by Fishers rule using the logratio approach to compositional data.

Usage

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

## S3 method for class 'daFisher'
print(x, ...)

## S3 method for class 'daFisher'
predict(object, ..., newdata)

## S3 method for class 'daFisher'
summary(object, ...)

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” estimation.
plotScore	TRUE, if the scores should be plotted automatically.
...	additional arguments for the print method passed through
object	object of class “daFisher”
newdata	new data in the appropriate form (CoDa, etc)

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 coordinates and clr coefficients. 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.

Value

an object of class “daFisher” including the following elements

B	Between variance of the groups
W	Within variance of the groups
loadings	loadings
scores	fisher scores
mc	table indicating misclassifications
mcrate	misclassification rate
coda	coda
grp	grouping
grppred	predicted groups
xc	xc
meanj	meanj
cv	cv
pj	pj
meanov	meanov
fdiscr	fdiscr

Author(s)

Peter Filzmoser, Matthias Templ.

References

Filzmoser, P. and Hron, K. and Templ, M. (2012) Discriminant analysis for compositional data and robust parameter estimation. Computational Statistics, 27(4), 585-604.

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

## toy data (non-compositional)
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
summary(d2)
predict(d2, newdata = X)

## example with olive data:
## Not run: 
data(olive, package = "RnavGraph")
# exclude zeros (alternatively impute them if 
# the detection limit is known using impRZilr())
ind <- which(olive == 0, arr.ind = TRUE)[,1]
olives <- olive[-ind, ]
x <- olives[, 4:10]
grp <- olives$Region # 3 groups
res <- daFisher(x,grp)
res
summary(res)
res <- daFisher(x, grp, plotScore = TRUE)
res <- daFisher(x, grp, method = "robust")
res
summary(res)
predict(res, newdata = x)
res <- daFisher(x,grp, plotScore = TRUE, method = "robust")

# 9 regions
grp <- olives$Area
res <- daFisher(x, grp, plotScore = TRUE)
res
summary(res)
predict(res, newdata = x)

## End(Not run)

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.