How to initialize the parameter mu to zero of a Gaussian Mixture model ?

X = mat_cell;

        [counts,binLocations] = imhist(X);
        stem(binLocations, counts, 'MarkerSize', 1 );
        xlim([-1 1]); 
        % inital kmeans step used to initialize EM
        K = 2;               % number of mixtures/clusters
        rng('default');
        cInd = kmeans(X(:), K,'MaxIter', 75536);
        % fit a GMM model
        options = statset('MaxIter', 75536); 
        gmm = fitgmdist(X(:), K,'Start',cInd,'CovarianceType','diagonal','Regularize',1e-5,'Options',options);

Here X is the input matrix and I would like to initialize only the sigma parameter of the GMM to zero. How can i proceed?

Answer 1

[Richard Marveldoss]

I see that you have used the 'Start' argument to initialize your Gaussian Mixture model. Instead of using 'Start' with an array that contains mapping of the observation to its label in which case you cannot specify mu and sigma as they are computed from the result of kmeans operation. You can try to explicitly specify the mu and sigma parameter by using a structure whose field elements are mu and sigma. Also, the documentation for the fitgmdist contains an example where the mu and sigma are initialized manually. Link to the documentation: https://www.mathworks.com/help/stats/fitgmdist.html. Additionally, I have attached an example code based on your code to get you started where I have assumed a random dataset for X.

dataLength = 5000;
muData = [5 30];
stdData = [4 10];
X = [muData(1) + stdData(1)*randn(dataLength/2,1);  muData(2) + stdData(2)*randn(dataLength/2,1)];
[counts,binLocations] = imhist(X);
stem(binLocations, counts, 'MarkerSize', 1 );
xlim([-1 1]); 
% inital kmeans step used to initialize EM
K = 2;               % number of mixtures/clusters
rng('default');
[~,cInd.mu] = kmeans(X(:), K,'MaxIter', 75536);
% fit a GMM model
gmInitialVariance = 0.1;
initialSigma = cat(3,gmInitialVariance,gmInitialVariance)
% cInd.mu=[0;0];            %%if you want to initialize the mu parameter to 0.
cInd.Sigma=initialSigma;
options = statset('MaxIter', 75536); 
gmm = fitgmdist(X(:), K,'Start',cInd,'CovarianceType','diagonal','Regularize',1e-5,'Options',options);

[A. P. B.]

This is for univariate gaussian distribution?? How can it be done for multivariate gaussian distribution

Answer 2

[Richard Marveldoss]

For a multivariate Gaussian distribution, the manner in which you construct your input datasets will vary. For example ,the below documentation contains a example where a dataset is generated using two bivariate Gaussian distribution. https://www.mathworks.com/help/stats/fitgmdist.html#examples