## EM Algorithm for Gaussian Mixture Model (EM GMM)

Version 1.16.0.1 (4.71 KB) by
EM algorithm for Gaussian mixture.

Updated 5 Dec 2018

This package fits Gaussian mixture model (GMM) by expectation maximization (EM) algorithm.It works on data set of arbitrary dimensions.
Several techniques are applied to improve numerical stability, such as computing probability in logarithm domain to avoid float number underflow which often occurs when computing probability of high dimensional data.
The code is also carefully tuned to be efficient by utilizing vertorization and matrix factorization.

This algorithm is widely used. The detail can be found in the great textbook "Pattern Recognition and Machine Learning" or the wiki page
http://en.wikipedia.org/wiki/Expectation-maximization_algorithm

This function is robust and efficient yet the code structure is organized so that it is easy to read. Please try following code for a demo:
close all; clear;
d = 2;
k = 3;
n = 500;
[X,label] = mixGaussRnd(d,k,n);
plotClass(X,label);

m = floor(n/2);
X1 = X(:,1:m);
X2 = X(:,(m+1):end);
% train
[z1,model,llh] = mixGaussEm(X1,k);
figure;
plot(llh);
figure;
plotClass(X1,z1);
% predict
z2 = mixGaussPred(X2,model);
figure;
plotClass(X2,z2);

Besides using EM to fit GMM, I highly recommend you to try another submission of mine: Variational Bayesian Inference for Gaussian Mixture Model
(http://www.mathworks.com/matlabcentral/fileexchange/35362-variational-bayesian-inference-for-gaussian-mixture-model) which performs Bayesian inference on GMM. It has the advantage that the number of mixture components can be automatically identified by the algorithm.

Upon request, I also provide a prediction function for out-of-sample inference.

This function is now a part of the PRML toolbox (http://www.mathworks.com/matlabcentral/fileexchange/55826-pattern-recognition-and-machine-learning-toolbox)
For anyone who wonders how to finish his homework, DONT send email to me.

### Cite As

Mo Chen (2023). EM Algorithm for Gaussian Mixture Model (EM GMM) (https://www.mathworks.com/matlabcentral/fileexchange/26184-em-algorithm-for-gaussian-mixture-model-em-gmm), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2009b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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#### EmGm

Version Published Release Notes
1.16.0.1

improve description

1.16.0.0

Update description
tweak and add prediction function
update title, description, and tag

1.15.0.0

tuning

1.13.0.0

Fix several minor bugs and reorganize the code structure a bit.

1.12.0.0

update loggausspdf due to api change of matlab

1.11.0.0

reorganize and clean the code a bit

1.10.0.0

fix bug for 1d data

1.8.0.0

fix bug for 1d data

1.7.0.0

Fixed missing file

1.3.0.0

update description

1.2.0.0