Gaussian mixture model sometimes seems to fit very badly

Kshitij Singh answered . 2025-04-26 06:19:47

Hi cyclist,

the default starting values are selected from the data at random, and you have discovered that this sometimes does not work well. There's an argument 'replicates' that you can use to have it try this multiple times and deliver the bone fit. However, in more recent releases including R2014b there is a new argument 'Start','plus' that uses a better starting method, one based on the kmeans++ algorithm for clustering. Here's a variant of your function that shows the relative performance of the default random start and the 'plus' start:

N = 100000;
EFFECT_SIZE = 5;
seedList = 1:20;
means1 = zeros(length(seedList),2);
means2 = zeros(length(seedList),2);
for s = seedList
    s
    rng(s)
    X = [randn(N,1); randn(N,1)+EFFECT_SIZE];
    rng(s)  % randomness is used in the fit also
    GMModel = fitgmdist(X,2);
    means1(s,:) = GMModel.mu';
    rng(s)
    GMModel = fitgmdist(X,2,'start','plus');
    means2(s,:) = GMModel.mu';
end
plot(means1(:,1),means1(:,2),'bx',means2(:,1),means2(:,2),'ro')

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