As was remarked earlier, it is found experimentally that the EM algorithm, although very fashionable, is very vulnerable to initialisation, and converges at a rate somewhat slower than a slug bungee-jumping in treacle. Given the effective limits of precision of computers, this can simply lead to wrong answers, as was shown earlier.
Reasons for preferring EM are that it does, given good initialisation, lead to a Maximum Likelihood solution in many cases. Thus one can feel at peace with statisticians and probabilists, and assuage one's conscience about the optimality of the classification. To those who have read the last chapter, this has about as much force as chanting mantras and using garlic to keep vampires at bay, but the unreflective need all the confidence and certainty about life they can get. In some cases, the constrained optimisation problem which is what finding the Maximum Likelihood solution amounts to for a mixture model, can be solved by traditional methods, usually involving some numerical work and Newton's Method. I shall not go into this approach because it is found that with reasonable initialisation, EM works reasonably well, and I shall have something to say about Neural Model methods of accomplishing this a little later.