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### Highlights from EM algorithm for Gaussian mixture model with background noise

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# EM algorithm for Gaussian mixture model with background noise

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### Andrew (view profile)

16 May 2012 (Updated )

Standard EM algorithm to fit a GMM with the (optional) consideration of background noise.

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Description

This is the standard EM algorithm for GMMs, presented in Bishop's book "Pattern Recognition and Machine Learning", Chapter 9, with one small exception, the addition of a uniform distribution to the mixture to pick up background noise/speckle; data points which one would not want to associate with any cluster.

NOTE: This function requires the MATLAB Statistical Toolbox and, for plotting the ellipses, the function error_ellipse, available from http://www.mathworks.com/matlabcentral/fileexchange/4705. Also requires at least MATLAB 7.9 (2009b)

For a demo example simply run GM_EM();
Plotting is provided automatically for 1D/2D cases with 5 GMs or less.

Usage: % GM_EM - fit a Gaussian mixture model to N points located in n-dimensional space.
% GM_EM(X,k) - fit a GMM to X, where X is N x n and k is the number of
% clusters. Algorithm follows steps outlined in Bishop
% (2009) 'Pattern Recognition and Machine Learning', Chapter 9.

% Optional inputs
% bn_noise - allow for uniform background noise term ('T' or 'F',
% default 'T'). If 'T', relevant classification uses the
% (k+1)th cluster
% reps - number of repetitions with different initial conditions
% (default = 10). Note: only the best fit (in a likelihood sense) is
% returned.
% max_iters - maximum iteration number for EM algorithm (default = 100)
% tol - tolerance value (default = 0.01)

% Outputs
% idx - classification/labelling of data in X
% mu - GM centres

Acknowledgements

Em Algorithm For Gaussian Mixture Model inspired this file.

Required Products Statistics Toolbox
MATLAB
MATLAB release MATLAB 7.9 (R2009b)

08 Aug 2014 David Provencher

### David Provencher (view profile)

I'm trying to run the code, but I keep getting this warning :

'Warning: chol failed, algorithm abandoned';

because the cholcov(Sigma(:,:,j),0); line always fails at the 2nd iteration (bn_noise='T') or 3rd iteration (bn_noise='F').

FYI, I have no NaN values in my data, and I get coherent results with kmeans() and emgm() [the submission that inspired this one]. Actually, no matter what data I feed into the function (e.g. squre matrix, rand(m,n), ...) this step always fails.

Any insight on this?
Thanks,
David

Comment only
01 Oct 2012 Jin Wang

### Jin Wang (view profile)

the input has to be square,right?
if my input data is not square, like 200x10, what should I do?
Thanks!

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16 May 2012 peter

### peter (view profile)

an "unknown" cluster, this is what we have been looking for. thanks a lot.