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SUMMARY:Clusters Everywhere: A tour of cluster analysis and its applicatio
n + Model-based Clustering with Sparse Covariance Matrices
DTSTART;VALUE=DATE-TIME:20211019T073000Z
DTEND;VALUE=DATE-TIME:20211019T093000Z
DTSTAMP;VALUE=DATE-TIME:20220524T062643Z
UID:indico-event-7129@indico.math.cnrs.fr
DESCRIPTION:First Part Clusters Everywhere: A tour of cluster analysis and
its application\n\nThis talk will give an overview of cluster analysis\,
including some history of the development of clustering\, approaches taken
and examples of its application in science\, medicine and social science.
\n\nSecond Part Model-based Clustering with Sparse Covariance Matrices\n\n
Finite Gaussian mixture models are widely used for model-based clustering
of continuous data. Nevertheless\, since the number of model parameters sc
ales quadratically with the number of variables\, these models can be easi
ly over-parameterized. For this reason\, parsimonious models have been dev
eloped via covariance matrix decompositions or assuming local independence
. However\, these remedies do not allow for direct estimation of sparse co
variance matrices nor do they take into account that the structure of asso
ciation among the variables can vary from one cluster to the other. To thi
s end\, we introduce mixtures of Gaussian covariance graph models for mode
l-based clustering with sparse covariance matrices. A penalized likelihood
approach is employed for estimation and a general penalty term on the gra
ph configurations can be used to induce different levels of sparsity and i
ncorporate prior knowledge. Model estimation is carried out using a struct
ural-EM algorithm for parameters and graph structure estimation\, where tw
o alternative strategies based on a genetic algorithm and an efficient ste
pwise search are proposed for inference. With this approach\, sparse compo
nent covariance matrices are directly obtained. The framework results in a
parsimonious model-based clustering of the data via a flexible model for
the within-group joint distribution of the variables. Extensive simulated
data experiments and application to illustrative datasets show that the me
thod attains good classification performance and model quality. This work
was completed with Michael Fop and Luca Scrucca\n\n \n\nhttps://indico.ma
th.cnrs.fr/event/7129/
LOCATION:Lyon1\, Doua 112
URL:https://indico.math.cnrs.fr/event/7129/
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