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observed. For the case of clustering multidimensional numerical data that can be
modeled as a Gaussian mixture, it turns out that the best way to think of the
unobserved data is in terms of a sequence of random variables, one for each observed
data point, whose values dictate the selection of the Gaussian for that data point.
This point is explained in great detail in my on-line tutorial at
L<https://engineering.purdue.edu/kak/Tutorials/ExpectationMaximization.pdf>.

The EM algorithm in our context reduces to an iterative invocation of the following
steps: (1) Given the current guess for the means and the covariances of the different
Gaussians in our mixture model, use Bayes' Rule to update the posterior class
probabilities at each of the data points; (2) Using the updated posterior class
probabilities, first update the class priors; (3) Using the updated class priors,
update the class means and the class covariances; and go back to Step (1).  Ideally,
the iterations should terminate when the expected log-likelihood of the observed data
has reached a maximum and does not change with any further iterations.  The stopping
rule used in this module is the detection of no change over three consecutive
iterations in the values calculated for the priors.

This module provides three different choices for seeding the clusters: (1) random,
(2) kmeans, and (3) manual.  When random seeding is chosen, the algorithm randomly
selects C<K> data elements as cluster seeds.  That is, the data vectors associated
with these seeds are treated as initial guesses for the means of the Gaussian