R/B_GC.IDX.R

In BayesCVI: Bayesian Cluster Validity Index

B_GC.IDX <- function(x, kmax, indexlist = "all", method = 'FCM', fzm = 2,
                   iter = 100, nstart = 20,
                   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(indexlist %in% c("all", "GC1", "GC2", "GC3", "GC4")))
    stop("Argument 'indexlist' is not in 'all', 'GC1', 'GC2', 'GC3', 'GC4'")
  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
  gc1 = vector()
  gc2 = vector()
  gc3 = vector()
  gc4 = vector()
  distance =dist(x,diag = TRUE,upper= TRUE)
  dd = as.matrix(distance)
  dd[lower.tri(dd)] = 0
  diag(dd) = 0
  # For checking IDX
  Check_GC1 = sum(indexlist %in% c("all","GC1"))>=1
  Check_GC2 = sum(indexlist %in% c("all","GC2"))>=1
  Check_GC3 = sum(indexlist %in% c("all","GC3"))>=1
  Check_GC4 = sum(indexlist %in% c("all","GC4"))>=1

  # 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
    n = nrow(x)
    mt = t(m)
    NI = colSums(m)
    nws = floor(sum(NI*(NI-1)/2))

    # GC1: sum product
    if(Check_GC1){
      PD1 = m%*%mt
      G1 = sum(PD1*dd)
      Gmax1 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD1[lower.tri(PD1)],decreasing = T)[1:nws])
      Gmin1 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD1[lower.tri(PD1)],decreasing = F)[1:nws])
      gc1[k-kmin+1] = (G1-Gmin1)/(Gmax1-Gmin1)
    }

    if(sum(indexlist %in% c("all","GC2","GC3","GC4"))>=1){
      PD2 = matrix(rep(0,n^2),n,n)
      PD3 = matrix(rep(0,n^2),n,n)
      PD4 = matrix(rep(0,n^2),n,n)
      for (s in 1:n){
        #GC2: sum-min
        if(Check_GC2){
          PD2[s,] =  colSums(pmin(mt,m[s,]))
        }
        # GC3: max-product
        if(Check_GC3){
          PD3[s,] = apply(m[s,]*mt,2,max)
        }
        # GC4: max-min
        if(Check_GC4){
          PD4[s,] = apply(pmin(mt,m[s,]),2,max)
        }
      } # end loop s
      if(Check_GC2){
        G2 = sum(PD2*dd)
        Gmax2 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD2[lower.tri(PD2)],decreasing = T)[1:nws])
        Gmin2 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD2[lower.tri(PD2)],decreasing = F)[1:nws])
        gc2[k-kmin+1] = (G2-Gmin2)/(Gmax2-Gmin2)
      }
      if(Check_GC3){
        G3 = sum(PD3*dd)
        Gmax3 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD3[lower.tri(PD3)],decreasing = T)[1:nws])
        Gmin3 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD3[lower.tri(PD3)],decreasing = F)[1:nws])
        gc3[k-kmin+1] = (G3-Gmin3)/(Gmax3-Gmin3)
      }
      if(Check_GC4){
        G4 = sum(PD4*dd)
        Gmax4 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD4[lower.tri(PD4)],decreasing = T)[1:nws])
        Gmin4 = sum(sort(dd,decreasing = T)[1:nws]*sort(PD4[lower.tri(PD4)],decreasing = F)[1:nws])
        gc4[k-kmin+1] = (G4-Gmin4)/(Gmax4-Gmin4)
      }
    }# END GC index
  }#end k loop
  if(any(indexlist %in% "all")){
    indexlist = paste0("GC",seq(4))
  }
  GC.list = list()
  for (idx in seq(length(indexlist))) {
    CVI.dframe = data.frame("C" = kmin:kmax,"Index" = get(tolower(indexlist[idx])))
    maxGI = max(CVI.dframe[,"Index"]) # The smallest value of the GI indicates the optimal number of cluster
    rk = (maxGI - CVI.dframe[,"Index"])/sum(maxGI - CVI.dframe[,"Index"])
    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",paste0(indexlist[idx]))
    list.re = list("BCVI" = BCVI,"VAR" = VarBCVI,"Index" = CVI.dframe)
    assign(paste0(indexlist[idx],"_list"),list.re)
    GC.list[[paste0(indexlist[idx])]] = get(paste0(indexlist[idx],"_list"))
  }
  if (sum(indexlist == "all")==1){
    return(GC.list)
  } else {
    return(GC.list[indexlist])
  }
}