1d:T7f2,# SEPARATON INFORMATION MATRIX Separation information matrix containing the nearest neighbor and farthest neighbor of each cluster. ```r nearestNeighborSepVal(sepValMat) ``` ## Arguments - `sepValMat`: a `K` by `K` matrix, where `K` is the number of clusters. `sepValMat[i,j]` is the separation index between cluster `i` and `j`. ## Returns This function returns a separation information matrix containing `K` rows and the following six columns, where `K` is the number of clusters. - **Column 1:**: Labels of clusters ($1, 2, \ldots, numClust$), where $numClust$ is the number of clusters for the data set. - **Column 2:**: Labels of the corresponding nearest neighbors. - **Column 3:**: Separation indices of the clusters to their nearest neighboring clusters. - **Column 4:**: Labels of the corresponding farthest neighboring clusters. - **Column 5:**: Separation indices of the clusters to their farthest neighbors. - **Column 6:**: Median separation indices of the clusters to their neighbors. ## References Qiu, W.-L. and Joe, H. (2006a) Generation of Random Clusters with Specified Degree of Separaion. **Journal of Classification**, 23 (2), 315-334. Qiu, W.-L. and Joe, H. (2006b) 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) n3 <- 30 mu3 <- c(10, 10) Sigma3 <- matrix(c(3, 1.5, 1.5, 1), 2, 2) projDir <- c(1, 0) muMat <- rbind(mu1, mu2, mu3) SigmaArray <- array(0, c(2, 2, 3)) SigmaArray[, , 1] <- Sigma1 SigmaArray[, , 2] <- Sigma2 SigmaArray[, , 3] <- Sigma3 tmp <- getSepProjTheory( muMat = muMat, SigmaArray = SigmaArray, iniProjDirMethod="SL") sepValMat <- tmp$sepValMat nearestNeighborSepVal(sepValMat = sepValMat) ```

nearestNeighborSepVal function