R/sc.R

In zcebeci/fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

sc <- function(x, u, v, m, t=NULL, eta, tidx ="f"){
  if(missing(x))
    stop("Missing input argument. A ppclust object or a numeric data set is required")
  tidx <- match.arg(tidx, c("e","f","g"))
  if(inherits(x, "ppclust")){
    X <- as.matrix(x$x)
    if(!is.null(x$u)){
      U <- as.matrix(x$u)
      m <- x$m
    }
    else if(!is.null(x$t)){
      U <- as.matrix(x$t)
      m <- x$eta
    }
    else{
      stop("Argument 'x' does not have the fuzzy membership or typicality matrix")
    }
    V <- as.matrix(x$v)
    if(tidx == "e" || tidx == "g"){
      if(!is.null(x$t)){
        T <- x$t
        eta <- x$eta
      }
      else
        stop("Argument 'x' does not have the typicality matrix")
    }
    dcheck <- FALSE
  }
  else{
    dcheck <- TRUE
    if(!missing(x))
      if(is.matrix(x) || is.data.frame(x) || is.vector(x))
        X <- as.matrix(x)
      else
         stop("Argument 'x' must be a valid instance of the 'ppclust', a numeric vector, data frame or matrix")
    else
      stop("Missing argument 'x'")
    if(!missing(u))
      if(is.matrix(u) || is.data.frame(u))
        U <- as.matrix(u)
      else
        stop("Argument 'u' must be a numeric data frame or matrix")
    else
      stop("Missing argument 'u'")
    if(!missing(v))
      if(is.matrix(v) || is.data.frame(v))
        V <- as.matrix(v)
      else
        stop("Argument 'v' must be a numeric data frame or matrix")
    else
      stop("Missing argument 'v'")
    if(tidx != "f")
      if(!is.null(t))
        if(is.matrix(t) || is.data.frame(t))
          T <- as.matrix(t)
        else
          stop("Argument 't' must be a numeric data frame or matrix")
      else
        stop("Argument 't' is null")
    if(tidx != "f"){
      if(missing(eta))
        eta <- 2 
      if(!is.numeric(eta))
        stop("Argument 'eta' must be number") 
      if(eta < 1)
        stop("Argument 'eta' should be a positive number equals to or greater than 1") 
    }
    if(missing(m))
      m <- 2 
    if(!is.numeric(m))
      stop("Argument 'm' must be number") 
    if(m < 1)
      stop("Argument 'm' should be a positive number equals to or greater than 1") 
  }
  if(nrow(X) != nrow(U))
    stop("The number of rows of data set is not equal to the number of rows of the membership matrix")
  if(ncol(X) != ncol(V))
    stop("The number of columns of the data set matrix is not equal to the number of columns of prototypes matrix")
  if(ncol(U) != nrow(V))
    stop("The number of columns of the membership matrix is not equal to the number of rows of prototypes matrix")
  if(tidx == "g"){
    if(!is.null(T))
      U <- T/rowSums(T)
    else
      stop("Typicality matrix is required to compute the generalized SC index")
  }
  n <- nrow(U)
  k <- ncol(U)
  vcenters <- apply(V, 2, mean)
  idx <- as.double(0)
  tnomsc1 <- tdenomsc1 <- 0
  for(j in 1:k){
    denomsc1 <- 0
    totu <- 0
    for(i in 1:n){
      if(tidx=="e"){
        denomsc1 <- denomsc1 + (U[i,j]^m + T[i,j]^eta) * sum((X[i,]-V[j,])^2) 
        totu <- totu + U[i,j] + T[i,j]
      }
      else{
        denomsc1 <- denomsc1 + (U[i,j]^m) * sum((X[i,]-V[j,])^2) 
        totu <- totu + U[i,j]
      }
    }
    tnomsc1 <- tnomsc1 + sum((V[j,]-vcenters)^2)
    tdenomsc1 <- tdenomsc1 + denomsc1 / totu
  }
  sc1 <- tnomsc1 / k / tdenomsc1
  tsqminu <- tminu <- 0
  for(j in 1:(k-1)){
    for(l in (j+1):k){
      for(i in 1:n){
        if(tidx=="e")
          minu <- min((U[i,j]+T[i,j]), (U[i,l]+T[i,l]))
        else
          minu <- min(U[i,j], U[i,l])
        tsqminu <- tsqminu + minu^2
        tminu <- tminu + minu
      }
    }
  }
  tsqmaxu <- tmaxu <- 0
  for(i in 1:n){
    if(tidx=="e"){
      tsqmaxu <- tsqmaxu + max((U[i,]+T[i,]))^2
      tmaxu <- tmaxu + max((U[i,]+T[i,]))
    }
    else{
      tsqmaxu <- tsqmaxu + max(U[i,])^2
      tmaxu <- tmaxu + max(U[i,])
    }
  }
  sc2 <- (tsqminu/tminu) / (tsqmaxu/tmaxu)
  idx <- sc1 - sc2
  if(tidx == "f")
    names(idx) <- "sc"
  else if(tidx == "e")
    names(idx) <- "sc.e"
  else if(tidx == "g")
    names(idx) <- "sc.g"
  return(idx)
}