How to create a Gaussian mixed model (GMM) with many components?

Hi, I have a series of 1D data which is in the histogram. I want to use a GMM equivalent model for this data. I have written the following code, can you guide me in the continuation of this code?

clear all ; close all ; clc

warning off ;

load Data

% type 1: section [1,37,78,187,249,288,364,396,451,532,563,607]

X = 1:607 ;

D = D(X) ;

ft = fittype( 'smoothingspline' );

opts = fitoptions( 'Method', 'SmoothingSpline' );

opts.SmoothingParam = 0.015;

[SF, ~] = fit( X', D, ft, opts );

D = SF(X) ;

D = normalize(D-min(D),'norm') ;

%% Get Data from bar

figure ;

B = bar(X,D,'EdgeColor','none') ; hold on

Y = B.YData ;

%% peak clusters

[P data] = findpeaks(-Y+max(Y),'MinPeakWidth',4.5,'MinPeakDistance',10) ; % 'WidthReference','halfheight'

plot(data,P,'vg') ; data = data' ;

indexSep = [1 data' length(X)] ;

K = length(indexSep)-1 ;

index = zeros(size(X)) ;

for i=1:K

index(indexSep(i):indexSep(i+1)) = i ;

end

index = index' ;

%% Show Clusters

G = {'r*','b*','g*','k*','c*','y*','m*','ro','bo','go','ko','co','yo'} ;

for i = 1:K

plot(X(index==i),Y(index==i),[G{i}])

end

%% Does it need weight?

%% fit components

Model = 'a*exp(-((x-b)/c)^2)' ;

for i = 1:K

opts = fitoptions( 'Method', 'NonlinearLeastSquares','MaxIter', 500,'Robust','Bisquare');

needindex = find(maxk(Y(index==i),1)==Y(index==i)) ;

opts.StartPoint = [max(Y(index==i)) indexSep(i)+X(needindex(1)) (max(X(index==i))-min(X(index==i)))/2];

opts.Lower = [max(Y(index==i))-5 opts.StartPoint(2)-10 0] ;

opts.Upper = [max(Y(index==i))+5 opts.StartPoint(2)+10 Inf] ;

f = fit(X(index==i)',Y(index==i)',Model,opts) ;

AICoeff = coeffnames(f) ;

AIValue = cellstr(num2str(coeffvalues(f)')) ;

fs = replace(Model,AICoeff,AIValue) ;

fs = replace(fs,{'--','-+','+-','++','*','^'},{'+','-','-','+','.*','.^'}) ;

eval(['F' num2str(i) ' = fs ;'])

eval(['f' num2str(i) ' = inline(F' num2str(i) ') ;'])

% need fit with full sum(FK)

end

%% Show

newx = -400:1200 ;

for i = 1:K

eval(['newy(' num2str(i) ',:) = f' num2str(i) '(newx) ;'])

plot(newx,newy(i,:),'LineWidth',1,'Color','k')

end

axis([X(1)-10 X(end)+10 0 max(Y)])

%% In this section I want to see an equivalent GMM that matches this data

options = statset('MaxIter', 500);

gm = gmdistribution.fit(Y',K-1, 'Options', options);

gm = fitgmdist(Y',K) ;

y = pdf(gm,newx');

plot(newx,y,'LineWidth',2,'Color','r')

Indeed, I need a way to calculate GMM coefficients(correct gm.mu,gm.Sigma,\pi_{k}) and match each component.

[Mohamed Hassan]

add this part to your code:

ComponentMeans = gm.mu;
ComponentCovariance = gm.Sigma;
MixtureProportions = gm.ComponentProportion

I have a question please. Could I apply your code to an image? I wanna show the gaussian distributions on the histogram.