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

elongs to the j th cluster, and thus, they can be used to assign the observations to the
cluster with higher posterior probability.
This clustering model is also suitable for databases with large amounts of records (Brijs
et al., 2004). In fact, even with a very large database, the clustering is done without any
additional effort. In general, to examine the suitability of this algorithm, two issues
should be taken into account. These issues are the dimensions of the problem and the
covariance structure. In fact, it is well known that the speed of the EM algorithm
depends on the ‘missing’ information. One could measure the missing information as
the ratio of the observed information to the missing information, which is related to the
number of latent variables introduced. Adding more latent variables leads to more
‘missing’ information and thus adds more computing time.
The above fact is true as far as the number of dimensions is concerned (Brijs et al.,
2004). More dimensions lead to more latent variables. If the structure is not
complicated, the algorithm will perform relatively the same, but if the structure is more
complicated, then more computational effort is needed. In this thesis, the EM algorithm
is fully described for the case of two-way interactions (section 5.3.5.1).
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