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On the Geometry of EM algorithms

An understanding of a simple geometric argument that underlies all EM algorithms gives an appreciation for certain aspects of their behavior. Using several illustrative examples, this paper demonstrates how the geometry of EM algorithms can help explain how their rate of convergence is related to the proportion of missing data and how an EM algorithm can fail in a pathological case. This geometric intuition also helps explain why, contrary to a view expressed by some, there is no reason to exclude EM algorithms from cases in which the likelihood function is zero for certain values of the parameter.