R/NMI.R

In Ecological-Complexity-Lab/infomap_ecology_package: Community Detection using Infomap, Inspired by Ecological Networks

#' Normalized mutual information
#'
#' Calculate normalized mutual information based on a confusion matrix. Very
#' useful for comparing between two partition structures of a network.
#'
#' @param N A confusion matrix.
#'
#' @return Value between 0 (no mutual information) to 1 (complete mutual
#'   information).
#'
#' @details If the partitions are exactly the same then all the nodes that
#'   appear in a given module in the first network will also appear in the same
#'   module in the second network. In this case, the confusion matrix will have
#'   all the values on the diagonal, and NMI=1.
#'
#' @references Danon L, Díaz-Guilera A, Duch J, Arenas A. Comparing community
#'   structure identification. J Stat Mech. 2005;2005: P09008.
#' @references Guimerà R, Sales-Pardo M, Amaral LAN. Module identification in
#'   bipartite and directed networks. Phys Rev E Stat Nonlin Soft Matter Phys.
#'   2007;76: 036102.
#' @references Pilosof S, Fortuna MA, Cosson J-FC, Galan M, Kittipong C, Ribas
#'   A, et al. Host-parasite network structure is associated with
#'   community-level immunogenetic diversity. Nat Commun. 2014;5: 5172.
#'
#' @examples
#' # Generate a confusion martrix for a network with 50 modules. 
#' # Partition A has 6 modules (rows), partition B has 5 (columns).
#' # Each cell in N indicates the number of nodes that were assigned
#' # together to a module in A and B. For example, 5 nodes were assigned 
#' # to module 2 in partition A and to module 1 in partition B.
#' N <- matrix(0,6,5)
#' diag(N[-1,])<-c(5,2,6,5,5)
#' diag(N) <- c(4,4,6,5,5)
#' N[6,1] <- 2
#' N[1,4] <- 1
#' NMI(N)
#'
#' # An example of perfect information (exact same partitions):
#' N <- matrix(0,5,5)
#' diag(N) <- c(10,15,10,12,3)
#' NMI(N) # Should be 1
#'
#' @export
NMI <- function (N) {
  S <- sum(N)
  CA = dim(N)[1]; CB = dim(N)[2]
  Iup=0
  for (i in 1:CA){
    for (j in 1:CB){
      if (N[i,j] != 0){
        Ni.=sum(N[i,])
        N.j=sum(N[,j])
        Iup = Iup+N[i,j]*log((N[i,j]*S)/(Ni.*N.j))
      }
    }
  }
  Idown1=0;Idown2=0
  for (i in 1:CA){
    Ni.=sum(N[i,])
    Idown1=Idown1+Ni.*log(Ni./S)
  }
  for (j in 1:CB){
    N.j=sum(N[,j])
    Idown2=Idown2+N.j*log(N.j/S)
  }
  I=-2*Iup/(Idown1+Idown2)

  return(I)
}