  In the mixture modeling frame, this paper presents the polynomial Gaussian
cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate
data, in a twofold way. Firstly, it allows for possible nonlinear dependencies
in the mixture components by considering a polynomial regression. Secondly, it
is not restricted to be used for model-based clustering only being
contextualized in the most general model-based classification framework.
Maximum likelihood parameter estimates are derived using the EM algorithm and
model selection is carried out using the Bayesian information criterion (BIC)
and the integrated completed likelihood (ICL). The paper also investigates the
conditions under which the posterior probabilities of component-membership from
a polynomial Gaussian CWM coincide with those of other well-established
mixture-models which are related to it. With respect to these models, the
polynomial Gaussian CWM has shown to give excellent clustering and
classification results when applied to the artificial and real data considered
in the paper.
