R/B_PBM.IDX.R

In BayesCVI: Bayesian Cluster Validity Index

B_PBM.IDX <- function(x, kmax, method = "FCM",
                    fzm = 2, nstart = 20, iter = 100,
                    alpha = "default",
                    mult.alpha = 1/2){
  if(missing(x))
    stop("Missing input argument. A numeric data frame or matrix is required")
  if(missing(kmax))
    stop("Missing input argument. A maximum number of clusters  is required")
  if(!is.numeric(kmax))
    stop("Argument 'kmax' must be numeric")
  if(kmax > nrow(x))
    stop("The maximum number of clusters for consideration should be less than or equal to the number of data points in dataset.")
  if(!any(method  == c("FCM","EM")))
    stop("Argument 'method' should be one of 'FCM','EM' ")
  if(method == "FCM"){
    if(fzm <= 1)
      stop("Argument 'fcm' should be the number greater than 1",call. = FALSE)
    if(!is.numeric(nstart))
      stop("Argument 'nstart' must be numeric")
    if(!is.numeric(iter))
      stop("Argument 'iter' must be numeric")
  }
  if(!is.numeric(mult.alpha))
    stop("Argument 'mult.alpha' must be numeric")
  n = nrow(x)
  kmin = 2 #fix value
  if(any(alpha %in% "default")){
    alpha = rep(1,length(kmin:kmax))
  }
  if(length(kmin:kmax) != length(alpha)) # check
    stop("The length of kmin to kmax must be equal to the length of alpha")
  adj.alpha = alpha*(n)^mult.alpha
  # Defined vector
  pbm = vector()
  # start k loop
  for(k in kmin:kmax){
    if(method == "EM"){ # EM Algorithm
      EM.model <- Mclust(x,G=k,verbose=FALSE)
      assign("m",EM.model$z)
      assign("c",t(EM.model$parameters$mean))
    }else if(method == "FCM"){ # FCM Algorithm
      wd = Inf
      # cm.out = list()
      for (nr in 1:nstart){
        FCM.model = cmeans(x,k,iter,verbose=FALSE,method="cmeans",m=fzm)
        if (FCM.model$withinerror < wd){
          wd = FCM.model$withinerror
          FCM.model2 =FCM.model
        }
      }
      assign("m",FCM.model2$membership)
      assign("c",FCM.model2$centers)
    }
    # Defined variable
    d3 = vector()
    n = nrow(x)
    d7 = sqrt(rowSums((x-matrix(colMeans(x),n,ncol(x),byrow=T))^2)) #NW
    d8 = vector()
    d9 = vector()
    for (j in 1:k){
      center = matrix(c[j,],n,ncol(x),byrow = T)
      d8[j] = (m[,j])%*%sqrt(rowSums((x-center)^2))
    }
    s=1
    for(i in 1:(k-1)){
      for(j in (i+1):k){
        d3[s]=sum((c[i,]-c[j,])^2)
        d9[s]= sqrt(d3[s]) #NW
        s=s+1
      }
    }
    pbm[k-kmin+1] = ((1/k)*(sum(d7)*max(d9)/sum(d8)))^2
  } #end loop if for indexes based on compactness and seperated
  CVI.dframe = data.frame("C" = kmin:kmax,"Index" = pbm)
  minGI = min(CVI.dframe[,"Index"]) # The largest value of the GI indicates the optimal number of cluster
  rk = (CVI.dframe[,"Index"] - minGI)/sum(CVI.dframe[,"Index"] - minGI)
  nrk = n*rk
  ex = (adj.alpha + nrk) / (sum(adj.alpha)+ n)
  var = ((adj.alpha+nrk)*(sum(adj.alpha)+n - adj.alpha - nrk))/((sum(adj.alpha)+n)^2*(sum(adj.alpha)+n+1))
  BCVI = data.frame("k" = kmin:kmax,"BCVI" = ex)
  VarBCVI = data.frame("k" = kmin:kmax,"Var" = var)
  colnames(CVI.dframe) = c("k","PBM")
  S_PBM.result = list("BCVI" = BCVI,"VAR" = VarBCVI,"Index" = CVI.dframe)
  return(S_PBM.result)
}