R/RankDistance.R

In Rankcluster: Model-Based Clustering for Multivariate Partial Ranking Data

#' The Kendall distance between two ranks is the number of pairs that are in different order in the two ranks.
#' @title Kendall distance between two ranks
#' @author Julien Jacques
#' @param x,y two ranks of size m. 
#' @param type type of the rank representation ("ordering" ou "ranking"). 
#' @return an integer, the Kendall distance between x and y.
#' @references A New Measure of Rank Correlation, M. G. Kendall
#' @examples
#' x <- 1:5
#' y <- c(2, 3, 1, 4, 5)
#' distKendall(x, y, type = "ordering")
#' @export

distKendall<- function(x, y, type = "ordering")
{
  if(type=="ordering")
    dist=distKendall_ordering(x,y)
  else 
    dist=distKendall_ranking(x,y)
  
  return(dist)	
}

distKendall_ranking<- function(x, y)
{
  m = length(x)
  distKendall_ranking=0
  for (i in 1:(m-1))
  {
    for (j in (i+1):m)
    {
      if (((x[i]-x[j])*(y[i]-y[j]))<0)
      {
        distKendall_ranking=distKendall_ranking+1
      }
    }
  }
  return(distKendall_ranking)
}



distKendall_ordering<- function(x, y)
{
  m = length(x)
  distKendall_ordering=0
  x_ordering=x
  y_ordering=y
  for (i in 1:m)
  {
    x_ordering[i]=which(x==i)
    y_ordering[i]=which(y==i)
  }
  distKendall_ordering=distKendall_ranking(x_ordering,y_ordering)
  return(distKendall_ordering)
}

#' The Spearman distance is the square of Euclidean distance between two rank vector.
#' @title Spearman distance between two ranks
#' @author Julien Jacques
#' @param x,y two ranks of size m. 
#' @return an integer, the Spearman distance between x and y.
#' @examples
#' x <- 1:5
#' y <- c(2, 3, 1, 4, 5)
#' distSpearman(x,y)
#' @export

distSpearman<- function(x, y)
{
  distSpearman=sum((x-y)^2)
  return(distSpearman)
}

# CorrelSpearman calculates the Spearman rank correlation between two ranks.
# @title Spearman rank correlation coefficient
# @author Julien Jacques
# @param x,y two ranks of size m. 
# @return a real, the Spearman rank correlation between x and y.
# @examples
# x=1:5
# y=c(2,3,1,4,5)
# CorrelSpearman(x, y)
# @export
CorrelSpearman<- function(x, y)
{
  CorrelSpearman=sqrt(sum((x-y)^2))
  return(CorrelSpearman)
}

#' The Cayley distance between two ranks x and y is the minimum number of transpositions required to transform the ranking x into y.
#' @title Cayley distance between two ranks
#' @author Julien Jacques
#' @param x,y two ranks of size m.
#' @return the Cayley distance between x and y.
#' @examples
#' x <- 1:5
#' y <- c(2, 3, 1, 4, 5)
#' distCayley(x, y)
#' @export
distCayley<- function(x, y)
{
  m = length(x)
  distCayley=0
  for (i in 1:(m-1))
  {
    if (! x[i]==y[i])
    {
      distCayley=distCayley+1
      tmp=x[i]
      x[i]=y[i]
      x[which(y[i]==x)]=tmp
    }	    
  }
  return(distCayley)
}


#' The Hamming distance between two ranks x and y is the number of difference between the two ranks.
#' For example, the Hamming's distance between x=(1,4,2,5,3) and y=(1,3,4,5,2) is 3 because, only 1 and 5 have the same place in both ranks.
#' @title Hamming distance between two ranks
#' @author Julien Jacques
#' @param x,y two ranks of size m. 
#' @return an integer, the Hamming distance between x and y.
#' @examples
#' x <- 1:5
#' y <- c(2, 3, 1, 4, 5)
#' distHamming(x, y)
#' @export
distHamming<- function(x, y)
{
  m = length(x)
  distHamming=0
  for (i in 1:m)
  {
    if (! x[i]==y[i])
    {
      distHamming=distHamming+1
    }	    
  }
  return(distHamming)
}