I found the popular convergence proof of the EM algorithm is wrong because Q may and should decrease in some E steps; P(Y|X) from the E-step is also improper Shannon's channel.
For details, see my paper https://arxiv.org/abs/1810.11227
A counterexample where Q may and Should decrease for faster convergence.
There is an example, in which Q can pass through Q-smaller and Q-larger areas to reach Q* that maximizes observed imcomplete data log-likelihood L.
An initialization map for selecting means:
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