sepIndex function

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

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

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.

Returns

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

References

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

Author(s)

Weiliang Qiu weiliang.qiu@gmail.com

Harry Joe harry@stat.ubc.ca

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)