GetNMI.m

function NMI = GetNMI(A,B)
% call: 
% 
%         NMI = getNMI(A,B)
%         
% This function computes the Normalized Mutual Information (NMI) between 
% 2 modular partitions or community structures given in vectors A and B.
% NMI is a measure of the similarity between the two graph partitions, and 
% its interpretation follows that of canonical Mutual Information, i.e. 
% assuming that I have complete knowledge of partition A, how much knowledge 
% can I get, from A, about partition B? If A and B are identical, then 
% NMI = 1, whereas if A and B are independent, NMI --> 0.
% 
% INPUT
% 
%      A    :   Community partition of graph A *
%      B    :   Community partition of graph B *
% 
%      * A and B are N-length vectors, where each i-th element is the integer 
%        labeling the k-th community to which node i-th was assigned.
%        
%        
% OUTPUT
% 
%      NMI  :   Normalized Mutual Information 
%      
%      
%     
% References:
% [1] Kuncheva & Hadjitodorov, 2004, IEEE Intern. Conf. on Syst. Man and Cybern.
% [2] Alexander-Bloch et al., 2012, NeuroImage
% 
% 
% R. G. Bettinardi
% ------------------------------------------------------------------------------------------------------------------------------------------------------------
if nargin < 2
    error('One of the two inputs is missing !!!')
end
% ASSURE A; B INTEGERS!        
N  = numel(A);
Ca = max(A);
Cb = max(B);
N1 = zeros(Ca*Cb,1);
D1 = zeros(Ca,1);
D2 = zeros(Cb,1);
n1_k = 0;
for i = 1:Ca
    
    N_idot   = sum(A==i);
    D1(i) = N_idot * log(N_idot/N);
    
   for j = 1:Cb 
       
       n1_k = n1_k + 1;
       
       N_dotj = sum(B==j);
       N_ij   = sum(((A==i) + (B==j))==2);
       
       if N_ij == 0
           N1(n1_k) = 0;
       else
           N1(n1_k) = N_ij * log( (N_ij*N)/(N_idot*N_dotj)  );
       end
       
       D2(j) = N_dotj * log(N_dotj/N);
       
   end
end
NMI = (-2 * sum(N1) ) / ( sum(D1) + sum(D2) );