NMI: Normalized mutual information

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

Normalized mutual information

Description

Calculate normalized mutual information based on a confusion matrix. Very useful for comparing between two partition structures of a network.

Usage

NMI(N)

Arguments

N	A confusion matrix.

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.

Value

Value between 0 (no mutual information) to 1 (complete mutual information).

References

Danon L, Díaz-Guilera A, Duch J, Arenas A. Comparing community structure identification. J Stat Mech. 2005;2005: P09008.

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.

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

Ecological-Complexity-Lab/infomap_ecology_package documentation built on June 6, 2024, 5:28 a.m.