R/HierarchicalSC.R

In sClust: R Toolbox for Unsupervised Spectral Clustering

#' @title Hierarchical Spectral Clustering
#' @author Emilie Poisson Caillault and Erwan Vincent
#' @description 
#' @param W Gram Similarity Matrix.
#' @param K number of cluster to obtain.
#' @param method method that will be used in the hierarchical clustering.
#' @param flagDiagZero if True, Put zero on the similarity matrix W.
#' @param verbose To output the verbose in the terminal.
#' @return returns a list containing the following elements:
#' \itemize{
#'  \item{cluster: }{a vector containing the cluster}
#'  \item{eigenVect: }{a vector containing the eigenvectors}
#'  \item{eigenVal: }{a vector containing the eigenvalues}
#' }
#' @references Sanchez-Garcia, R., Fernnelly, M. and al. (2014). Hierarchical Spectral Clustering of Power Grids. In IEEE Transaction on Power Systems 29.5, pages 2229-2237. ISSN : 0885-8950.
#' @examples
#' ### Example 1: 2 disks of the same size
#' n<-100 ; r1<-1
#' x<-(runif(n)-0.5)*2;
#' y<-(runif(n)-0.5)*2
#' keep1<-which((x*2+y*2)<(r1*2))
#' disk1<-data.frame(x+3*r1,y)[keep1,]
#' disk2 <-data.frame(x-3*r1,y)[keep1,]
#' sameTwoDisks <- rbind(disk1,disk2)
#' W <- compute.similarity.ZP(scale(sameTwoDisks))
#' res <- HierarchicalSC(W,K=2,method = "ward.D2",flagDiagZero=TRUE,verbose=TRUE)
#' plot(sameTwoDisks, col = res$cluster)
#' plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space",
#'      xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+');
#' plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); 
#' 
#' ### Example 2: Speed and Stopping Distances of Cars
#' W <- compute.similarity.ZP(scale(iris[,-5]))
#' res <- HierarchicalSC(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE)
#' plot(iris, col = res$cluster)
#' plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space",
#'      xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+');
#' plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); 
HierarchicalSC <- function(W, K=5, method = "ward.D2", flagDiagZero=FALSE, verbose = FALSE){
  
  #Checking the similarity matrix
  W <- checking.gram.similarityMatrix(W, flagDiagZero=flagDiagZero, verbose = verbose)
  
  #Compute the laplacian
  laplacianResult <- compute.laplacian.NJW(W, verbose = verbose)
  
  #K Eigenvectors selection
  if(verbose){message(paste(K, " EIGEN VECTORS SELECTION"))}
  V <- laplacianResult$eigen$vector[,1:K]
  
  #normalization with sphere projection if more than one cluster
  if(verbose){message("NORMALIZATION OF EIGENVECTOR")}
  Y <- V/apply(V,MARGIN=1,FUN=function(x) norm(matrix(x),"f"))
  if(verbose){
    message("NORMALIZED K EIGEN VECTORS = ")
    print(Y)
  }
  
  #Hierarchical clustering
  if(verbose){message("CALCULATION OF THE GRAPH")}
  graph <- hclust(dist(Y), method = method)
  if(verbose){plot(graph)}
  
  #Cutting the result graph
  if(verbose){message("CUTTING THE GRAPH")}
  cluster <- cutree(graph,K)
  if(verbose){cat("cluster = ", cluster, "\n")}
  
  out <- list(cluster = cluster, eigenVect = laplacianResult$eigen$vector, eigenVal = laplacianResult$eigen$values)
}