function [B_g] = fowlkes_mallows_index(lab1,lab2)
% FOWLKES_MALLOWS_INDEX - Implements the Fowlkes-Mallows cluster index for various clusterings
% 
% Inputs: 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-11-05
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

n = length(lab1);

N = mk_matching_matrix_N(lab1,lab2);

% compute T_g: 
Nsquared       = N.^2; 
NsquaredSummed = sum(Nsquared(:)); 
T_g            = NsquaredSummed - n; 

% compute n_{i \dot}
n_idot = sum( N, 2 ); 

% compute n_{\dot j}
n_dotj = sum( N, 1 ); 

% compute P_g: 
P_g = sum( n_idot.^2 ) - n; 

% compute Q_g: 
Q_g = sum( n_dotj.^2 ) - n; 

% compute B_g: 
B_g = T_g / sqrt( P_g * Q_g );