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

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WinCento99
WinCento99 2021-10-9
评论： Mohamed Hassan 2022-6-22
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.
  1 个评论
Mohamed Hassan
Mohamed Hassan 2022-6-22
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.

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