multivariate poisson hidden markov models for analysis of spatial ...

Another alternative is to use the partitioning of a k-means clustering as the initial
starting values (McLachlan et al., 1988).
• The EM algorithm generally converges very slowly when compared to other
iterative algorithm, such as Newton-Raphson algorithm. The EM converges
linearly towards the optimum, while Newton-Raphson converges with quadratic
speed towards optimum (Aitkin and Aitkin, 1996).
• Non-convergence to global optimum sometimes is another problem of the EM
algorithm. Convergence and the properties of convergence depend heavily on
the starting values.
• An important problem, but somewhat ignored in the literature, is the stopping
rule for the number of iterations. In fact, the EM is rather sensitive in the sense
that different stopping rules can lead to different estimates (Seidel et al., 2000).
According to Karlis and Xekalaki (1998), this is caused because at every
iteration, the loglikelihood increases by a very small amount and at the same
time the estimates can change a lot.
• Even though the EM is more popular, its general principles are well understood
and extensively used algorithm, in every problem one has to build the algorithm
in a different way.
5.3.4 Determining the number of components or states
In some applications of model-based clustering, there is enough information about the
number of components k in the mixture model to be specified with sufficient certainty.
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