13,718 research outputs found
Enhancing the selection of a model-based clustering with external qualitative variables
In cluster analysis, it can be useful to interpret the partition built from
the data in the light of external categorical variables which were not directly
involved to cluster the data. An approach is proposed in the model-based
clustering context to select a model and a number of clusters which both fit
the data well and take advantage of the potential illustrative ability of the
external variables. This approach makes use of the integrated joint likelihood
of the data and the partitions at hand, namely the model-based partition and
the partitions associated to the external variables. It is noteworthy that each
mixture model is fitted by the maximum likelihood methodology to the data,
excluding the external variables which are used to select a relevant mixture
model only. Numerical experiments illustrate the promising behaviour of the
derived criterion
Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model
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
Mixtures of Shifted Asymmetric Laplace Distributions
A mixture of shifted asymmetric Laplace distributions is introduced and used
for clustering and classification. A variant of the EM algorithm is developed
for parameter estimation by exploiting the relationship with the general
inverse Gaussian distribution. This approach is mathematically elegant and
relatively computationally straightforward. Our novel mixture modelling
approach is demonstrated on both simulated and real data to illustrate
clustering and classification applications. In these analyses, our mixture of
shifted asymmetric Laplace distributions performs favourably when compared to
the popular Gaussian approach. This work, which marks an important step in the
non-Gaussian model-based clustering and classification direction, concludes
with discussion as well as suggestions for future work
- …