# The revised silhouette This function returns a revised silhouette plot, cluster centers in weighted squared Euclidean distances and a matrix containing the weighted squared Euclidean distances between cases and each cluster center. Missing values are adjusted. ```r revisedsil(d,reRSKC=NULL,CASEofINT=NULL,col1="black", CASEofINT2 = NULL, col2="red", print.plot=TRUE, W=NULL,C=NULL,out=NULL) ``` ## Arguments - `d`: A numerical data matrix, `N` by `p`, where `N` is the number of cases and `p` is the number of features. - `reRSKC`: A list output from RSKC function. - `CASEofINT`: Necessary if print.plot=TRUE. A vector of the case indices that appear in the revised silhouette plot. The revised silhouette widths of these indices are colored in `col1` if `CASEofINT != NULL`. The average silhouette of each cluster printed in the plot is computed EXCLUDING these cases. - `col1`: See `CASEofINT`. - `CASEofINT2`: A vector of the case indices that appear in the revised silhouette plot. The indices are colored in `col2`. - `col2`: See `CASEofINT2` - `print.plot`: If `TRUE`, the revised silhouette is plotted. - `W`: Necessary if `reRSKC = NULL`. A positive real vector of weights of length `p`. - `C`: Necessary if `reRSKC = NULL`. An integer vector of class labels of length `N`. - `out`: Necessary if `reRSKC = NULL`. Vector of the case indices that should be excluded in the calculation of cluster centers. In `RSKC`, cluster centers are calculated without the cases that have the furthest 100*`alpha` % Weighted squared Euclidean distances to their closest cluster centers. If one wants to obtain the cluster centers from `RSKC` output, set `out` = `$oW`. ## Returns - **trans.mu**: Cluster centers in reduced weighted dimension. See example for more detail. - **WdisC**: `N` by `ncl` matrix, where `ncl` is the prespecified number of clusters. It contains the weighted distance between each case and all cluster centers. See example for more detail. - **sil.order**: Silhouette values of each case in the order of the case index. - **sil.i**: Silhouette values of cases ranked by decreasing order within clusters. The corresponding case index are in `obs.i` ## Author(s) Yumi Kondo ## References Yumi Kondo (2011), Robustificaiton of the sparse K-means clustering algorithm, MSc. Thesis, University of British Columbia [http://hdl.handle.net/2429/37093](http://hdl.handle.net/2429/37093) ## Examples ```r # little simulation function sim <- function(mu,f){ D<-matrix(rnorm(60*f),60,f) D[1:20,1:50]<-D[1:20,1:50]+mu D[21:40,1:50]<-D[21:40,1:50]-mu return(D) } ### output trans.mu ### p<-200;ncl<-3 # simulate a 60 by p data matrix with 3 classes d<-sim(2,p) # run RSKC re<-RSKC(d,ncl,L1=2,alpha=0.05) # cluster centers in weighted squared Euclidean distances by function sil sil.mu<-revisedsil(d,W=re$weights,C=re$labels,out=re$oW,print.plot=FALSE)$trans.mu # calculation trans.d<-sweep(d[,re$weights!=0],2,sqrt(re$weights[re$weights!=0]),FUN="*") class<-re$labels;class[re$oW]<-ncl+1 MEANs<-matrix(NA,ncl,ncol(trans.d)) for ( i in 1 : 3) MEANs[i,]<-colMeans(trans.d[class==i,,drop=FALSE]) sil.mu==MEANs # coincides ### output WdisC ### p<-200;ncl<-3;N<-60 # generate 60 by p data matrix with 3 classes d<-sim(2,p) # run RSKC re<-RSKC(d,ncl,L1=2,alpha=0.05) si<-revisedsil(d,W=re$weights,C=re$labels,out=re$oW,print.plot=FALSE) si.mu<-si$trans.mu si.wdisc<-si$WdisC trans.d<-sweep(d[,re$weights!=0],2,sqrt(re$weights[re$weights!=0]),FUN="*") WdisC<-matrix(NA,N,ncl) for ( i in 1 : ncl) WdisC[,i]<-rowSums(scale(trans.d,center=si.mu[i,],scale=FALSE)^2) # WdisC and si.wdisc coincides ```

revisedsil function