Local Optima in EM
The GMM log-likelihood surface is non-concave with many stationary points (including permutations of the same solution), and EM is a hill climber that converges to whichever local maximum its initialization feeds it — hence multiple restarts keeping the best final likelihood.
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The GMM log-likelihood surface is non-concave with many stationary points (including permutations of the same solution), and EM is a hill climber that converges to whichever local maximum its initialization feeds it — hence multiple restarts keeping the best final likelihood.
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