Ji Hoon Jeong asked . 2022-04-02

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

mu
sigma
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

Using makedist('Normal') to create each gaussian distribution.
Multiply by each component proportion
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 :)

gaussian mixture m... ., normalization , normal distribution , gaussian distribution , gmm

Expert Answer

John Williams answered . 2024-12-04 04:56:38

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.

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