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

5.3 Multivariate Poisson finite mixture models
The main idea (Vermunt et al., 2002 and McLachlan et al., 1988) in model-based
clustering, also known as latent class clustering or finite mixture models, is that the
observations (in our case weed counts) are assumed to be coming from a mixture of
density distributions for which the parameters of the distribution and the mixing
proportions and the number of the components are unknown. Therefore, the objective of
model-based clustering is to unmix the distributions and to find the most favorable
parameters of the distributions, and the number and the mixing proportions of the
components, given the underlying data (Fraley and Raftery, 1998).
The history of finite mixture models dates back to the late 19 th century (Pearson, 1894).
With the arrival of high-speed computers, the finite mixture models inventions began,
turning the attention to likelihood estimation of the parameters in a mixture distribution
(McLachlan et al., 1988). In particular, the explanation of the EM algorithm
(expectation_maximization) by Dempster et al., (1977) has given a new motivation to
the research of finite mixture models. Since then, a wide range of literature has been
published on this topic, even though most of publications date from 1985 and onwards
(Brijs, 2002).
Finite mixture models have demonstrated clustering in several practical applications,
including character recognition (Murtagh and Raftery, 1984); tissue segmentation
(Banfield and Raftery, 1993); minefield and seismic fault detection (Dasgupta and
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