MATLAB Examples

## Contents

clear, clc, close all hidden 

## First example of FSMEM : Fit a MVGM with default parameters

Calling FSMEM with the data Z only, without the knowledge of the number of compounds

% Generate MVGM %% d = 2; N = 2000; K_true = 5; clust_spread = 0.4; [M_true , S_true , P_true] = gene_mvgm(d , K_true , clust_spread); Z = sample_mvgm(N , M_true , S_true , P_true); logl_true = loglike_mvgm(Z , M_true , S_true , P_true); mdl_true = logl_true - 0.5*log(N)*K_true*((d+1) + d*((d+1))/2); % Display Orignal data %% offsetmin = [1.1 ; 0.9]; offsetmax = [0.9 ; 1.1]; pdf_true = pdf_mvgm(Z , M_true , S_true , P_true); minZ = min(Z , [] , 2); maxZ = max(Z , [] , 2); minZ = minZ.*offsetmin((sign(minZ) > 0)+1); maxZ = maxZ.*offsetmax((sign(maxZ) > 0)+1); vectx = minZ(1):0.1:maxZ(1); vecty = minZ(2):0.1:maxZ(2); [X , Y] = meshgrid(vectx , vecty); grid = [X(:) , Y(:)]'; pdf_support = pdf_mvgm(grid , M_true , S_true , P_true); figure(1) set(gcf , 'renderer' , 'opengl'); g = surfc(X , Y , reshape(pdf_support , length(vecty) , length(vectx))); alpha(g , 0.7); hold on h = stem3(Z(1 , :) , Z(2 , :) , pdf_true); hold off shading interp lighting phong light legend(h , '\bf{Z}') title(sprintf('Original data Z, K_{true} = %d, MDL(Z) = %8.3f' , K_true , mdl_true) , 'fontsize' , 12 , 'fontweight' , 'bold'); rotate3d on drawnow % FSMEM with unknown number of clusters % tic,[Mest , Sest , Pest , logl] = fsmem_mvgm(Z);,toc; K_est = size(Mest , 3); % Display Results % [x_true , y_true] = ndellipse(M_true , S_true); [x_est , y_est] = ndellipse(Mest , Sest); figure(2) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_est , y_est , 'r' , 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true)] , 'Z' , sprintf('True, K=%d' , K_true),sprintf('FSMEM, K=%d' , K_est)) title(sprintf('MDL(FSMEM) = %8.3f' , logl(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); disp(sprintf('\nK_true = %d , K_est = %d\n' , K_true , K_est)) disp(sprintf('pause\n')) 
Elapsed time is 0.592168 seconds. K_true = 5 , K_est = 5 pause 

## Second example of FSMEM : Fit a MVGM with default parameters & compare with the classical EM

Calling FSMEM with the data Z only, without the knowledge of the number of compounds
% Generate MVGM % d = 2; N = 1500; K_true = 5; clust_spread = 0.5; [M_true , S_true , P_true] = gene_mvgm(d , K_true , clust_spread); Z = sample_mvgm(N , M_true , S_true , P_true); logl_true = loglike_mvgm(Z , M_true , S_true , P_true); mdl_true = logl_true - 0.5*log(N)*K_true*((d+1) + d*((d+1))/2); % Display Orignal data % offsetmin = [1.1 ; 0.9]; offsetmax = [0.9 ; 1.1]; pdf_true = pdf_mvgm(Z , M_true , S_true , P_true); minZ = min(Z , [] , 2); maxZ = max(Z , [] , 2); minZ = minZ.*offsetmin((sign(minZ) > 0)+1); maxZ = maxZ.*offsetmax((sign(maxZ) > 0)+1); vectx = minZ(1):0.1:maxZ(1); vecty = minZ(2):0.1:maxZ(2); [X , Y] = meshgrid(vectx , vecty); grid = [X(:) , Y(:)]'; pdf_support = pdf_mvgm(grid , M_true , S_true , P_true); figure(3) set(gcf , 'renderer' , 'opengl'); g = surfc(X , Y , reshape(pdf_support , length(vecty) , length(vectx))); alpha(g , 0.7); hold on h = stem3(Z(1 , :) , Z(2 , :) , pdf_true); hold off shading interp lighting phong light legend(h , '\bf{Z}') title(sprintf('Original data Z, K_{true} = %d, MDL(Z) = %8.3f' , K_true , mdl_true) , 'fontsize' , 12 , 'fontweight' , 'bold'); rotate3d on drawnow % FSMEM with unknown number of clusters % tic,[Mest , Sest , Pest , logl ] = fsmem_mvgm(Z);,toc; K_est = size(Mest , 3); % Full EM with known and fixed number of clusters % % Calling FSMEM with flag fail_exit = 0 in the options structure run a single Full EM options.Kini = K_true; options.fail_exit = 0.0; tic,[Mestem , Sestem , Pestem , loglem] = fsmem_mvgm(Z , options);,toc % Display Results % [x_true , y_true] = ndellipse(M_true , S_true); [x_est , y_est] = ndellipse(Mest , Sest); [x_estem , y_estem] = ndellipse(Mestem , Sestem); figure(4) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_est , y_est , 'r' , 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true)] , 'Z' , sprintf('True, K=%d' , K_true),sprintf('FSMEM, K=%d' , K_est)) title(sprintf('MDL(FSMEM) = %8.3f' , logl(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); figure(5) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_estem , y_estem , 'r' , 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true)] , 'Z' , sprintf('True, K=%d' , K_true), 'EM') title(sprintf('MDL(EM) = %8.3f' , loglem(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); figure(6) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_est , y_est , 'r' , x_estem , y_estem , 'g', 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true) , h(2+K_true + K_est)] , 'Z' , sprintf('True, K=%d' , K_true),sprintf('FSMEM, K=%d' , K_est) , 'EM') title(sprintf('MDL(FSMEM) = %8.3f, MDL(EM) = %8.3f' , logl(1 , end) , loglem(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); 
Elapsed time is 1.216768 seconds. Elapsed time is 0.023764 seconds. 

## Third example of FSMEM : Fit a Elliptical MVGM with a given initial MVGM

Calling FSMEM with the data Z only, without knowing number of compounds

% Generate MVGM % d = 2; N = 2000; K_true = 8; P_true = permute((1/K_true)*ones(1 , K_true) , [1 3 2]); M_true = permute([1.5 , 1 , 0 , -1 , -1.5 , -1 , 0 , 1 ; 0 1 , 1.5 , 1 , 0 , -1 , -1.5 , -1] , [1 3 2]); S_true = cat(3 , diag([0.01 , 0.1]) , diag([0.1 , 0.1]) , diag([0.1 , 0.01]) , diag([0.1 , 0.1]) , diag([0.01 , 0.1]) , diag([0.1 , 0.1]) , diag([0.1 , 0.01]) , diag([0.1 , 0.1])); Z = sample_mvgm(N , M_true , S_true , P_true); logl_true = loglike_mvgm(Z , M_true , S_true , P_true); mdl_true = logl_true - 0.5*log(N)*K_true*((d+1) + d*((d+1))/2); % Display Orignal data % offsetmin = [1.1 ; 0.9]; offsetmax = [0.9 ; 1.1]; pdf_true = pdf_mvgm(Z , M_true , S_true , P_true); minZ = min(Z , [] , 2); maxZ = max(Z , [] , 2); minZ = minZ.*offsetmin((sign(minZ) > 0)+1); maxZ = maxZ.*offsetmax((sign(maxZ) > 0)+1); vectx = minZ(1):0.1:maxZ(1); vecty = minZ(2):0.1:maxZ(2); [X , Y] = meshgrid(vectx , vecty); grid = [X(:) , Y(:)]'; pdf_support = pdf_mvgm(grid , M_true , S_true , P_true); figure(7) set(gcf , 'renderer' , 'opengl'); g = surfc(X , Y , reshape(pdf_support , length(vecty) , length(vectx))); alpha(g , 0.7); hold on h = stem3(Z(1 , :) , Z(2 , :) , pdf_true); hold off shading interp lighting phong light legend(h , '\bf{Z}') title(sprintf('Original data Z, K_{true} = %d, MDL(Z) = %8.3f' , K_true , mdl_true) , 'fontsize' , 12 , 'fontweight' , 'bold'); rotate3d on % FSMEM with unknown number of clusters and fixed initial parameters% % [Mest , Sest , Pest , logl] = fsmem_mvgm(Z , [] , M_ini , S_ini , P_ini) % where K_ini clusters <> K_true are supposed for the initial parameter (M_ini , S_ini , P_ini) % Covariances by default are supposed to be full K_ini = 3; [M_ini , S_ini , P_ini] = init_mvgm(Z , K_ini); tic,[Mest , Sest , Pest , logl] = fsmem_mvgm(Z , [] , M_ini , S_ini , P_ini);,toc; K_est = size(Mest , 3); % Display Results % [x_true , y_true] = ndellipse(M_true , S_true); [x_est , y_est] = ndellipse(Mest , Sest); figure(8) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_est , y_est , 'r' , 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true)] , 'Z' , sprintf('True, K=%d' , K_true),sprintf('FSMEM, K=%d' , K_est)) title(sprintf('MDL(FSMEM) = %8.3f' , logl(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); % FSMEM with unknown number of clusters and initial parameters % % Here covariances are supposed to be elliptical <=> options.covtype = 1 % % [Mest , Sest , Pest , logl] = fsmem_mvgm(Z , options , M_ini , S_ini , P_ini) % clear options options.covtype = 1; tic,[Mest1 , Sest1 , Pest1 , logl1] = fsmem_mvgm(Z , options , M_ini , S_ini , P_ini);,toc; K_est1 = size(Mest1 , 3); % Display Results % [x_true , y_true] = ndellipse(M_true , S_true); [x_est1 , y_est1] = ndellipse(Mest1 , Sest1); figure(9) h = plot(Z(1 , :) , Z(2 , :) , '+' , x_true , y_true , 'k' , x_est1 , y_est1 , 'r' , 'linewidth' , 2); legend([h(1), h(2) , h(2+K_true)] , 'Z' , sprintf('True, K=%d' , K_true),sprintf('FSMEM, K=%d' , K_est1)) title(sprintf('MDL(FSMEM) = %8.3f' , logl1(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); 
Elapsed time is 2.048787 seconds. Elapsed time is 1.325096 seconds. 

## Fourth example of FSMEM : Fit spiral data %%

Calling FSMEM with special hyperparameters in options structure (a bit long even with the mex-file)

% Generate Spiral data % N = 3000; options.Kini = 20; options.Kmax = 40; options.maxite_fullem = 500; options.maxite_partialem = 500; options.epsi_fullem = 1e-7; options.epsi_partialem = 1e-7; options.maxcands_split = 12; options.maxcands_merge = 12; options.covtype = 0; Z = spiral2d(N); % Display Orignal data %% figure(10) plot(Z(1 , :) , Z(2 , :) , '+', 'linewidth' , 2) title('Original data Z' , 'fontsize' , 12 , 'fontweight' , 'bold'); drawnow % FSMEM with unknown number of clusters % % [Mest , Sest , Pest , logl ] = fsmem_mvgm(Z , options); tic,[Mest , Sest , Pest , logl] = fsmem_mvgm(Z , options);,toc K_est = size(Pest , 3); % Display Results % figure(11) [xest , yest] = ndellipse(Mest , Sest); [xaxes , yaxes] = ndellipse(Mest , Sest , [] , [] , 3); xaxes(end , :) = []; yaxes(end , :) = []; h = plot(Z(1 , :) , Z(2 , :) , '+' , xest , yest , 'r' , xaxes , yaxes , 'k', 'linewidth' , 2); legend([h(1), h(2) , h(2+K_est)] , 'Z' , sprintf('Estimated, K=%d' , K_est) , 'PC'); title(sprintf('MDL(FSMEM) = %8.3f' , logl(1 , end)) , 'fontsize' , 12 , 'fontweight' , 'bold'); 
Elapsed time is 52.220716 seconds.