sepIndex {clusterGeneration}

MEASURE THE MAGNITUDE OF THE GAP OR SPARSE AREA BETWEEN A PAIR OF CLUSTERS ALONG THE SPECIFIED PROJECTION DIRECTION

Description

Measure the magnitude of the gap or sparse area between a pair of clusters (or cluster distributions) along the specified projection direction.

Usage

sepIndexTheory(
	       projDir, 
	       mu1, 
	       Sigma1, 
	       mu2, 
	       Sigma2, 
               alpha = 0.05, 
	       eps = 1.0e-10, 
	       quiet = TRUE)

sepIndexData(
	     projDir, 
	     y1, 
	     y2, 
	     alpha = 0.05, 
	     eps = 1.0e-10, 
	     quiet = TRUE)

Arguments

projDir

Projection direction.

mu1

Mean vector of cluster 1.

Sigma1

Covariance matrix of cluster 1.

mu2

Mean vector of cluster 2.

Sigma2

Covariance matrix of cluster 2.

y1

Data matrix of cluster 1. Rows correspond to observations. Columns correspond to variables.

y2

Data matrix of cluster 2. Rows correspond to observations. Columns correspond to variables.

alpha

Tuning parameter reflecting the percentage in the two tails of a projected cluster that might be outlying. We set alpha=0.05 like we set the significance level in hypothesis testing as 0.05.

eps

Convergence threshold. A small positive number to check if a quantitiy q is equal to zero. If |q|<eps, then we regard q is equal to zero. eps is used to check if an algorithm converges. The default value is 1.0e-10.

quiet

A flag to switch on/off the outputs of intermediate results and/or possible warning messages. The default value is TRUE.

Value

The value of the separation index defined in Qiu and Joe (2006).

Author(s)

Weiliang Qiu [e-mail]
Harry Joe [e-mail]

References

Qiu, W.-L. and Joe, H. (2006) Separation Index and Partial Membership for Clustering. Computational Statistics and Data Analysis, 50, 585–603.

Examples

n1<-50
mu1<-c(0,0)
Sigma1<-matrix(c(2,1,1,5),2,2)
n2<-100
mu2<-c(10,0)
Sigma2<-matrix(c(5,-1,-1,2),2,2)
projDir<-c(1, 0)
sepIndexTheory(projDir, mu1, Sigma1, mu2, Sigma2)

library(MASS)
y1 <- mvrnorm(n1, mu1, Sigma1)
y2 <- mvrnorm(n2, mu2, Sigma2)
sepIndexData(
	     projDir = projDir, 
	     y1 = y1, 
	     y2 = y2)