Documentation>vl_demo_gmm_3d

# Source code for ``vl_demo_gmm_3d.m

This file is located in the ``toolbox/demo folder in VLFeat package.

    function vl_demo_gmm_3d
    % VL_DEMO_GMM_3D   Show how to initialize GMM learning with a custom set of modes

    %% Initialize points clustered in 3D
    numClusters = 5 ;
    dimension = 3 ;
    cc = hsv(numClusters) ;
    randn('state',0) ;
    X = [] ;
    for i=1:numClusters
      delta = 5*[i;0;0] ;
      %num = ceil(1000 / i) ;
      num = 500 ;
      s = diag([1,i, 1]) ;
      X = [X, bsxfun(@plus, s*randn(dimension, num), delta)] ;
    end

    %% Cluster using KMeans (ANN algorithm)
    elapsedKMEANS = tic ;
    vl_twister('state',0) ;
    [initMeans, assignments] = vl_kmeans(X, numClusters, ...
                                         'Verbose', ...
                                         'Algorithm', 'ann', ...
                                         'MaxNumIterations', 10, ...
                                         'Distance', 'l2', ...
                                         'NumTrees', 3, ...
                                         'MaxNumComparisons', 10);
    elapsedKMEANS = toc(elapsedKMEANS) ;
    fprintf('\n ---------- \n KMeans time - %f \n ---------- \n\n',elapsedKMEANS) ;

    %% Create initial GMM modes from KMeans clusters
    initSigmas = zeros(dimension,numClusters);
    initWeights = zeros(1,numClusters);

    figure(1) ; clf ;
    subplot(1,2,1) ; hold on ;

    for i=1:numClusters
      Xk = X(:,assignments==i) ;
      initWeights(i) = size(Xk,2) / numClusters ;

      plot3(Xk(1,:),Xk(2,:),Xk(3,:),'.','color',cc(i,:)) ;
      if size(Xk,1) == 0 || size(Xk,2) == 0
        initSigmas(:,i) = diag(cov(X'));
      else
        initSigmas(:,i) = diag(cov(Xk'));
      end
    end

    axis equal ;
    xlabel('x') ; ylabel('y') ; zlabel('z') ;
    title('GMM: KMeans intialization') ;

    %% Fit a GMM model to the maximum likelihood
    elapsedGMM = tic ;
    [means,sigmas,weights,ll,posteriors] = vl_gmm(X, numClusters, ...
                                                  'Initialization','custom', ...
                                                  'InitMeans',initMeans, ...
                                                  'InitCovariances',initSigmas, ...
                                                  'InitPriors',initWeights, ...
                                                  'Verbose', ...
                                                  'MaxNumIterations', 100) ;
    elapsedGMM = toc(elapsedGMM);
    fprintf('\n ---------- \n GMM time - %f \n ---------- \n',elapsedGMM) ;

    subplot(1,2,2) ; hold on ;
    [~,idx] = max(posteriors,[],1);
    for i=1:numClusters
      plot3(X(1,idx == i),X(2,idx == i),X(3,idx == i),'.','color',cc(i,:)) ;
    end

    axis equal ;
    xlabel('x') ; ylabel('y') ; zlabel('z') ;
    title('GMM: Estimated Gaussian mixture') ;