Separate Drawing of Gaussian Mixture Model

I have a 1D data which need to be separated by two .

So I used

    fitgmdist(data,2);

and got

1. mu
2. sigma
3. component proportion

for each of the gaussian distribution.

And here is the graph. (Gray : Data, Blue : psd of GMModel from fitgmdist)

Until here, everything was okay.

So, question.

How can I separate those two gaussian distribution graph?

I tried

1. Using makedist('Normal') to create each gaussian distribution.
2. Multiply by each component proportion
3. Add two distribution up

But somehow I wasn't able to get the same graph overlapping picture above.

Probably I have the wrong concept of "Normalization" or "Gaussian Mixture Model".

Any advise or site to lookup would be grateful.

------------------------------------------------------------ @Image Analyst: data uploaded. thanks for the advice I'll remember that next time :)

[Image Analyst]

Care to attach your data and code so people can try some things?

[Amr Hashem]

what is the code u use to fit the Gaussian of mixtures one dimentional?

[Trisha Kibaya]

Hi Ji Hoon Jeong, could you please share your codes? I am trying to get the same gaussian model on my one dimensional data but i'm not sure of what I am doing. Thanks a lot.

[Ji Hoon Jeong]

For your information, I just uploaded the same kind of my data file to this question. The uploaded '.mat' file has 3 variables,

• rawdata
• tabulated (tabulated = tabulate(round(data*10))
• GMModel (GMModel = fitgmdist(data,2))

The code I used to draw upper graph is below

 tabulated = tabulate(round(drawdata));
 bar(tabulated(:,1),tabulated(:,3)/100,'FaceColor','k');
 hold on;
 GMModel = fitgmdist(drawdata(:,1),2);
 plot(tabulated(:,1),pdf(GMModel,tabulated(:,1)),'Color','r','LineWidth',1);

I hope this helps you.

[Trisha Kibaya]

Thanks a lot, this helped a lot!

Answer 1

[Tom Lane]

You did something like this:

x = [randn(4000,1)/2; 5+2*randn(6000,1)];
f = fitgmdist(x,2);
histogram(x,'Normalization','pdf')
xgrid = linspace(-4,12,1001)';
hold on; plot(xgrid,pdf(f,xgrid),'r-'); hold off

You can duplicate the pdf values by doing something like this:

n1 = makedist('normal',f.mu(1),sqrt(f.Sigma(1)));
n2 = makedist('normal',f.mu(2),sqrt(f.Sigma(2)));
p = f.ComponentProportion;

y = p(1)*pdf(n1,xgrid) + p(2)*pdf(n2,xgrid);
hold on; plot(xgrid,y,'c--'); hold off

One thing to watch out for. In probability and statistics, it's common to write the standard deviation of a univariate normal distribution as the Greek letter sigma. But it's common to write the covariance matrix of a multivariate distribution as capital Sigma. So that's why I used sqrt(Sigma) to create the univariate distributions.

[Amr Hashem]

What is equivalent to "Makedist" as I am using Matlab 2012?

Answer 2

[yusra Ch]

Could you plz tell me how did you plot the bleu line in your graph ? I have GM that I want to draw but I dont know how to do it . could you plz help me?

gm =

Gaussian mixture distribution with 2 components in 1 dimensions

Component 1:

Mixing proportion: 0.500000

Mean: 3.3153

Component 2:

Mixing proportion: 0.500000

Mean: -61.5348

The values of Sigma are :

val(:,:,1) =

15.3648

val(:,:,2) =

137.2863

[Ji Hoon Jeong]

My code and question were related to how to fit raw data into a Gaussian Mixture Distribution, so it's bit different than your intention.

If you already know about the parameters of your distribution, than use the code below

% X range
xran = -10 : 0.1 : 10;
% Component 1
mu1 = 3.3153;
sigma1 = 15.3648;
proportion1 = 0.5;
% Component 2
mu2 = -61.5348;
sigma2 = 137.2863;
proportion2 = 0.5;
% plot the GMD
plot(xran, ...
    proportion1 * pdf('Normal', xran, mu1, sigma1) + proportion2 * pdf('Normal', xran, mu2, sigma2)...
    );

if the Sigma value you got is not the std, rather covariance matrix of a multivariate distribution, than uses this instead.

plot(xran, ...
    proportion1 * pdf('Normal', xran, mu1, sqrt(sigma1)) + proportion2 * pdf('Normal', xran, mu2, sqrt(sigma2))...
    );

Answer 3

[cynthia thing]

Hi , could you share the code for the histogram with fitted mixture model curve like the first picture above?

Much appreciated