covAxis {ICS}R Documentation

One step Tyler Shape Matrix

Description

This matrix can be used to get from ics the principal axes which is then known as principal axis analysis.

Usage

covAxis(X, na.action = na.fail)

Arguments

X numeric data matrix or dataframe.
na.action a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

The covAxis matrix V is a given for a sample of size n as

p ave{[(x_i-x_bar)S^{-1}(x_i-x_bar)']^(-1) (x_i-x_bar)'(x_i-x_bar)},

where x_bar is the mean vector and S the regular covariance matrix.

covAxis can be used to perform a Prinzipal Axis Analysis (Critchley et al. 2007) using the function ics. In that case for a centered data matrix X covAxis can be used as S2 in ics, where S1 should be in that case the regular covariance matrix.

Value

Matrix of the estimated scatter.

Author(s)

Klaus Nordhausen, klaus.nordhausen@uta.fi

References

Critchley , F., Pires, A. and Amado, C. (2007), Principal axis analysis, manuscript, ?, ?–?.

Tyler, D.E., Critchley, F., Dümbgen, L. and Oja, H. (2007), Invariant coordinate selecetion, submitted, ?, ?–?.

See Also

ics

Examples


data(iris)
iris.centered <- sweep(iris[,1:4], 2, colMeans(iris[,1:4]), "-")
iris.paa <- ics(iris.centered, cov, covAxis, stdKurt = FALSE)
summary(iris.paa)
plot(iris.paa, col=as.numeric(iris[,5]))    
mean(iris.paa@gKurt)
emp.align <- iris.paa@gKurt
emp.align

screeplot(iris.paa)
abline(h = 1)



[Package ICS version 1.2-0 Index]