Model-based clustering using copulas with applications

@article{Kosmidis2016ModelbasedCU,
  title={Model-based clustering using copulas with applications},
  author={Ioannis Kosmidis and Dimitris Karlis},
  journal={Statistics and Computing},
  year={2016},
  volume={26},
  pages={1079-1099}
}
The majority of model-based clustering techniques is based on multivariate normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas in model-based clustering offers two direct advantages over current methods: (i) the appropriate choice of copulas provides the ability to obtain a range of exotic shapes for the clusters, and (ii) the explicit choice of marginal distributions for the… 
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References

SHOWING 1-10 OF 60 REFERENCES
Model-based clustering with non-elliptically contoured distributions
TLDR
Finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions) are proposed, which start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties.
Copula Functions in Model Based Clustering
TLDR
This paper considers the other proposal based on the general stochastic approach in two versions: classification likelihood approach, where each observation comes from one of several populations; and mixture approach,where observations are distributed as a mixture of several distributions.
A Copula-Based Algorithm for Discovering Patterns of Dependent Observations
TLDR
A new algorithm (CoClust in brief) is proposed that allows to cluster dependent data according to the multivariate structure of the generating process without any assumption on the margins and is compared with a model–based clustering technique.
Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine
TLDR
The R package CDVine is presented which provides functions and tools for statistical inference of canonical vine (C-vine) and D-vine copulas and contains tools for bivariate exploratory data analysis and for b variables selection as well as for selection of pair-copula families in a vine.
Finite Mixture Models
TLDR
The aim of this article is to provide an up-to-date account of the theory and methodological developments underlying the applications of finite mixture models.
Model-based Gaussian and non-Gaussian clustering
TLDR
The classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms, including those based on the sum of squares criterion and on the criterion of Friedman and Rubin (1967), but it is restricted to Gaussian distributions and it does not allow for noise.
mclust Version 4 for R : Normal Mixture Modeling for Model-Based Clustering , Classification , and Density Estimation
TLDR
This version of mclust provides functions for parameter estimation via the EM algorithm for normal mixture models with a variety of covariance structures, and functions for simulation from these models.
Flexible mixture modelling using the multivariate skew-t-normal distribution
This paper presents a robust probabilistic mixture model based on the multivariate skew-t-normal distribution, a skew extension of the multivariate Student’s t distribution with more powerful
Multivariate mixture modeling using skew-normal independent distributions
...
...