comparison toolboxes/FullBNT-1.0.7/KPMtools/collapse_mog.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [new_mu, new_Sigma, new_Sigma2] = collapse_mog(mu, Sigma, coefs)
+% COLLAPSE_MOG Collapse a mixture of Gaussians to a single Gaussian by moment matching
+% [new_mu, new_Sigma] = collapse_mog(mu, Sigma, coefs)
+%
+% coefs(i) - weight of i'th mixture component
+% mu(:,i), Sigma(:,:,i) - params of i'th mixture component
+
+% S = sum_c w_c (S_c + m_c m_c' + m m' - 2 m_c m') 
+%   = sum_c w_c (S_c + m_c m_c') + m m' - 2 (sum_c m_c) m'
+%   = sum_c w_c (S_c + m_c m_c') - m m'
+
+new_mu = sum(mu * diag(coefs), 2); % weighted sum of columns
+
+n = length(new_mu);
+new_Sigma = zeros(n,n);
+new_Sigma2 = zeros(n,n);
+for j=1:length(coefs)
+  m = mu(:,j) - new_mu;
+  new_Sigma = new_Sigma + coefs(j) * (Sigma(:,:,j) + m*m');
+  new_Sigma2 = new_Sigma2 + coefs(j) * (Sigma(:,:,j) + mu(:,j)*mu(:,j)');
+end
+%assert(approxeq(new_Sigma, new_Sigma2 - new_mu*new_mu'))