www.pudn.com > gmm_utilities.zip > gmm_entropy.m

function p = gmm_entropy(g,N) 
 
g = gmm_normalise(g); 
 
if nargin == 2 
    p = gmm_entropy_montecarlo(g, N); 
else 
    p = gmm_entropy_unscented(g); 
end 
 
% 
% 
 
function p = gmm_entropy_montecarlo(g, N) 
% Monte Carlo approximation of entropy for Gaussian mixtures. 
s = gmm_samples(g, N); 
w = gmm_evaluate(g, s); 
p = -mean(log(w(w~=0))); 
 
% 
% 
 
function p = gmm_entropy_unscented(g) 
% Unscented gmm entropy, based on Goldberger's KLD approximation 
[D,N] = size(g.x);  
Ds = sqrt(D); 
 
p = 0; 
for i=1:N 
    Ps = Ds * matrix_square_root(g.P(:,:,i), 1); 
    x = repvec(g.x(:,i), D); 
    s = [x+Ps, x-Ps]; % unscented samples for i-th component of g 
     
    w = gmm_evaluate(g, s); 
    p = p - g.w(i)*sum(log(w));     
end 
p = p/(2*D); 
 
% 
% 
 
function R = matrix_square_root(P, type) 
switch type 
    case 1 % svd decomposition, P = U*D*U' = R*R' (UDU form is also called modified Cholesky decomposition) 
        [U,D,V] = svd(P); 
        R = U*sqrt(D); 
    case 2 % cholesky decomposition (triangular), P = R*R' 
        R = chol(P)'; 
    case 3 % principal square root (symmetric), P = R*R 
        R = sqrtm(P); 
end