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

function [gr, alpha] = gmm_covariance_intersect(g1, g2, alpha) 
% Conservative approx: Generalised covariance intersect 
% TODO: confirm this algorithms correctness. Does it make sense??? 
% Is there a measure of compactness that we can use to quantify how 
% conservative this is? say, entropy? 
%  
 
if nargin == 3 
    gr = gmm_covariance_intersect_alpha(g1, g2, alpha); 
else 
    alpha = fminbnd(@optimise_alpha, 0, 1, [], g1,g2); 
    gr = gmm_covariance_intersect_alpha(g1, g2, alpha); 
end 
 
% 
% 
 
function gr = gmm_covariance_intersect_alpha(g1, g2, alpha) 
 
D = size(g1.x, 1); 
M = size(g1.x, 2); 
N = size(g2.x, 2); 
R = M*N; 
 
gr.w = zeros(1, R); 
gr.x = zeros(D, R); 
gr.P = zeros(D, D, R); 
 
k = 1; 
for i=1:M 
    for j=1:N 
        [gr.x(:,k), gr.P(:,:,k), w] = covariance_intersect_weight(g1.x(:,i),g1.P(:,:,i), g2.x(:,j),g2.P(:,:,j), alpha); 
        gr.w(k) = g1.w(i) * g2.w(j) * w; 
         
        k = k+1; 
    end 
end 
 
% 
% 
 
function [x,P,w] = covariance_intersect_weight(x1,P1, x2,P2, alpha) 
[x,P] = covariance_intersect(x1,P1, x2,P2, alpha); 
w = weight_update(x1,P1, x2,P2, alpha); 
         
% 
% 
 
function w = weight_update(x1,P1, x2,P2, a) 
if a==0 | a==1, w = eps; return, end 
v = x1-x2; 
S = P1/a + P2/(1-a); 
%S = P1 + P2; 
w = gauss_evaluate(v, S); 
 
% 
% 
 
function w = optimise_alpha(alpha, g1,g2) 
% Optimise alpha according to various measures. I am not yet sure which is 
% the "right" one. For now, entropy and normalised determinant seem most promising. 
gr = gmm_covariance_intersect_alpha(g1, g2, alpha); 
gr = gmm_normalise(gr); 
switch 1 
    case 1 % Unscented entropy approximation 
        w = gmm_entropy(gr); 
    case 2 % Monte Carlo entropy approximation 
        w = gmm_entropy(gr, 100000); 
    case 3 % Sum of weighted determinants 
        w = 0; 
        for i=1:length(gr.w) 
            w = w + det(gr.P(:,:,i))*gr.w(i); 
        end 
    case 4 % Sum of normalised determinants 
        w = 0; 
        for i=1:length(gr.w) 
            w = w + det(gr.P(:,:,i))/gr.w(i); 
        end 
    otherwise 
        error('Invalid switch selection') 
end