www.pudn.com > FitFunc.zip > fit_mix_2D_gaussian.m

function [u,covar,t,iter] = fit_mix_2D_gaussian( X,M ) 
% 
% fit_mix_2D_gaussian - fit parameters for a 2D mixed-gaussian distribution using EM algorithm 
% 
% format:   [u,covar,t,iter] = fit_mix_2D_gaussian( X,M ) 
% 
% input:    X   - input samples, Nx2 vector 
%           M   - number of gaussians which are assumed to compose the distribution 
% 
% output:   u       - fitted mean for each gaussian (each mean is a 2x1 vector) 
%           covar   - fitted covariance for each gaussian. this is a 2x2xM matrix. 
%           t       - probability of each gaussian in the complete distribution 
%           iter    - number of iterations done by the function 
% 
 
% run with default values 
if ~nargin 
    M   = 1 + floor(rand*5); 
    for m = 1:M 
        D               = diag( rand(1,2)*10 );         % create a leagal cov matrix 
        A               = randn(2,2);                   % ...first choose the eigenvalues 
        A               = A/det(A);                     % ...and later, a random transform 
        covar(:,:,m)    = A*D*A';                       % ...the result -> cov matrix 
        u(:,m)          = randn(2,1)*5;                 % the mean of the gaussians 
        prob(m)         = rand;                         % each gaussian probability 
    end 
    X = build_mix_2D_gaussian( u,covar,prob,5000 );     % create the distribution samples 
    [u,covar,t,iter] = fit_mix_2D_gaussian( X,M );      % estimate it... 
    return 
end 
 
% set X dimensions 
if (size(X,2)~=2), 
    X = X.'; 
end 
 
% initialize and initial guesses 
N           = size( X,1 ); 
Z           = ones(N,M) * 1/M;                      % indicators vector 
P           = zeros(N,M);                           % probabilities vector for each sample and each model 
t           = ones(1,M) * 1/M;                      % distribution of the gaussian models in the samples 
u           = [linspace(min(X(:,1)),max(X(:,1)),M);... 
        linspace(min(X(:,2)),max(X(:,2)),M)];       % mean vector 
covar       = repmat( cov(X),[1,1,M] )/ sqrt(M);    %  vector of covariance matrices 
C           = 1/2/pi;                               % just a constant 
Ic          = ones(N,1);                            % - enable a row replication by the * operator 
Ir          = ones(1,2);                            % - enable a column replication by the * operator 
Q           = zeros(N,M);                           % user variable to determine when we have converged to a steady solution 
thresh      = 1e-3; 
step        = N; 
last_step   = inf; 
iter        = 0; 
min_iter    = 10; 
 
% main convergence loop, assume gaussians are 1D 
while ((( abs((step/last_step)-1) > thresh) & (step>(N*eps)) ) | (iter 1D vector 
    Q = Z; 
    for m = 1:M 
        S       = covar(:,:,m); 
        d       = det(S); 
        U       = u(:,m); 
        P(:,m)  = C ./ (Ic*d) .* exp( -1/2/d * (... 
            S(2,2)*(X(:,1)-U(1)).^2 + S(1,1)*(X(:,2)-U(2)).^2 - ... 
            (S(2,1)+S(1,2))*(X(:,1)-U(1)).*(X(:,2)-U(2)) ) ); 
        Z(:,m)  = (P(:,m)*t(m))./(P*t(:)); 
    end 
         
    % estimate convergence step size and update iteration number 
    prog_text   = sprintf(repmat( '\b',1,(iter>0)*12+ceil(log10(iter+1)) )); 
    iter        = iter + 1; 
    last_step   = step * (1 + eps) + eps; 
    step        = sum(sum(abs(Q-Z))); 
    fprintf( '%s%d iterations\n',prog_text,iter ); 
 
    % M step 
    % ======== 
    Zm              = sum(Z);               % sum each column 
    Zm(find(Zm==0)) = eps;                  % avoid devision by zero 
    t               = Zm/N; 
    for m = 1:M 
        dist        = X - Ic*(u(:,m)'); 
        covar(:,:,m)= dist' * ( (Z(:,m)*Ir) .* dist )/Zm(m);    % covariance estimation 
        u(:,m)      = (X')*Z(:,m) / Zm(m);                      % mean estimation 
    end 
end 
 
% plot the fitted distribution 
% ============================= 
plot_mix_gaussian( u,covar,t );