centroids: Group Centroids and (Pooled) Variances

In sda: Shrinkage Discriminant Analysis and CAT Score Variable Selection

Group Centroids and (Pooled) Variances

Description

centroids computes group centroids, the pooled mean and pooled variance, and optionally the group specific variances.

Usage

centroids(x, L, lambda.var, lambda.freqs, var.groups=FALSE, 
  centered.data=FALSE, verbose=TRUE)

Arguments

x	A matrix containing the data set. Note that the rows are sample observations and the columns are variables.
L	A factor with the group labels.
lambda.var	Shrinkage intensity for the variances. If not specified it is estimated from the data, see details below. lambda.var=0 implies no shrinkage and lambda.var=1 complete shrinkage.
lambda.freqs	Shrinkage intensity for the frequencies. If not specified it is estimated from the data. lambda.freqs=0 implies no shrinkage (i.e. empirical frequencies) and lambda.freqs=1 complete shrinkage (i.e. uniform frequencies).
var.groups	Estimate group-specific variances.
centered.data	Return column-centered data matrix.
verbose	Provide some messages while computing.

Details

As estimator of the variance we employ var.shrink as described in Opgen-Rhein and Strimmer (2007). For the estimates of frequencies we rely on freqs.shrink as described in Hausser and Strimmer (2009). Note that the pooled mean is computed using the estimated frequencies.

Value

centroids returns a list with the following components:

samples	a vector containing the samples sizes in each group,
freqs	a vector containing the estimated frequency in each group,
means	the group means and the pooled mean,
variances	the group-specific and the pooled variances, and
centered.data	a matrix containing the centered data.

Author(s)

Korbinian Strimmer (https://strimmerlab.github.io).

See Also

var.shrink, powcor.shrink.

Examples

# load sda library
library("sda")

## prepare data set
data(iris) # good old iris data
X = as.matrix(iris[,1:4])
Y = iris[,5]

## estimate centroids and empirical pooled variances
centroids(X, Y, lambda.var=0)
          
## also compute group-specific variances
centroids(X, Y, var.groups=TRUE, lambda.var=0)
   
## use shrinkage estimator for the variances
centroids(X, Y, var.groups=TRUE)

## return centered data
xc = centroids(X, Y, centered.data=TRUE)$centered.data
apply(xc, 2, mean)

## useful, e.g., to compute the inverse pooled correlation matrix
powcor.shrink(xc, alpha=-1)

sda documentation built on April 11, 2025, 6:16 p.m.