Mixtures with random covariates are statistical models which can beapplied for clustering and for density estimation of a random vector composed by a response variable and a set of covariates. In this class, the generalized linear Gaussian cluster-weghted model (GLGCWM) assumes, in each mixture component, an exponential family distribution for the response variable and a multivariateGaussian distribution for the vector of real-valued covariates. For parsimony sake, a family of fourteen models is here introduced by applying some constraints on the eigen-decomposed covariance matrices of the Gaussian distribution. The EM algorithm is described to find maximum likelihood estimates of the parameters forthese models. This novel family of models is finally applied to a real data set where a good classification performance is obtained, especially when compared with otherwell-established mixture-based approaches.

Parsimonious Generalized Linear Gaussian Cluster-Weighted Models

PUNZO, ANTONIO
;
INGRASSIA, Salvatore
2015-01-01

Abstract

Mixtures with random covariates are statistical models which can beapplied for clustering and for density estimation of a random vector composed by a response variable and a set of covariates. In this class, the generalized linear Gaussian cluster-weghted model (GLGCWM) assumes, in each mixture component, an exponential family distribution for the response variable and a multivariateGaussian distribution for the vector of real-valued covariates. For parsimony sake, a family of fourteen models is here introduced by applying some constraints on the eigen-decomposed covariance matrices of the Gaussian distribution. The EM algorithm is described to find maximum likelihood estimates of the parameters forthese models. This novel family of models is finally applied to a real data set where a good classification performance is obtained, especially when compared with otherwell-established mixture-based approaches.
2015
978-3-319-17376-4
Cluster-weighted models
Eigen decomposition
Generalized linear models
Model-based clustering
Parsimonious mixtures
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/57219
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