# 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. ```r 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 ```r 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) ```

sepIndex function