  The Expectation-Maximization (EM) algorithm is a commonly used method for
finding the maximum likelihood estimates of the parameters in a mixture model
via coordinate ascent. A serious pitfall with the algorithm is that in the case
of multimodal likelihood functions, it can get trapped at a local maximum. This
problem often occurs when sub-optimal starting values are used to initialize
the algorithm. Bayesian initialization averaging (BIA) is proposed as an
ensemble method to generate high quality starting values for the EM algorithm.
Competing sets of trial starting values are combined as a weighted average,
which is then used as the starting position for a full EM run. The method can
also be extended to variational Bayes (VB) methods, a class of algorithm
similar to EM that is based on an approximation of the model posterior. The BIA
method is demonstrated on real continuous, categorical and network data sets,
and the convergent log-likelihoods and associated clustering solutions
presented. These compare favorably with the output produced using competing
initialization methods such as random starts, hierarchical clustering and
deterministic annealing, with the highest available maximum likelihood
estimates obtained in a higher percentage of cases, at reasonable computational
cost. The implications of the different clustering solutions obtained by local
maxima are also discussed.
