Model-based clustering via linear cluster-weighted models

Ingrassia, Salvatore; Minotti, Simona C.; Punzo, Antonio

doi:10.1016/j.csda.2013.02.012

Cited by 83 publications

(56 citation statements)

References 33 publications

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“…For example, Ingrassia, Minotti, and Vittadini (2012) consider an extension to t-distribution that leads to the linear t-CWM. Ingrassia, Minotti, and Punzo (2014) introduce a family of 12 parsimonious linear t-CWMs, Punzo (2014) introduces the polynomial Gaussian CWM, Punzo and Ingrassia (2015a) propose CWMs for bivariate data of mixed type, and Punzo and Ingrassia (2015b) propose a family of 14 parsimonious linear Gaussian CWMs. Punzo and McNicholas (2014a) use a contamination approach for linear Gaussian CWMs.…”

Section: Cluster-weighted Modelsmentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

185

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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Section: Cluster-weighted Modelsmentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

185

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“…Moreover, in the same paper, the linear t-CWM was introduced considering both p (y|x, Ω g ) and p (x|Ω g ) to be t-distributed; again, mixture of t distributions and mixtures of regression models with t errors can be considered as nested in the linear t-CWM. Subsequently, Ingrassia, Minotti and Punzo (2014) presented a family of twelve CWMs, nested in the linear t-CWM, for model-based clustering. Subedi, Punzo, Ingrassia, and McNicholas (2013) addressed the problem of applicability of the CWM in high-dimensional X-spaces by assuming latent factors for the covariates in each mixture component.…”

Section: Introductionmentioning

confidence: 99%

Erratum to: The Generalized Linear Mixed Cluster-Weighted Model

et al. 2015

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Abstract:Cluster-weighted models (CWMs) are a flexible family of mixture models for fitting the joint distribution of a random vector composed of a response variable and a set of covariates. CWMs act as a convex combination of the products of the marginal distribution of the covariates and the conditional distribution of the response given the covariates. In this paper, we introduce a broad family of CWMs in which the component conditional distributions are assumed to belong to the exponential family and the covariates are allowed to be of mixed-type. Under the assumption of Gaussian covariates, sufficient conditions for model identifiability are provided. Moreover, maximum likelihood parameter estimates are derived using the EM algorithm. Parameter recovery, classification assessment, and performance of some information criteria are investigated through a broad simulation design. An application to real data is finally presented, with the proposed model outperforming other well-established mixture-based approaches.

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“…This method has improved robustness to noisy data. Following Ingrassia et al (2012), Ingrassia et al (2014) develop a family of twelve mixture models each inheriting from a linear t-cluster weighted model. Such models allow the group assignments to depend on the covariates and the component distributions to feature heavier than normal tails.…”

Section: Introductionmentioning

confidence: 99%

Mixtures of quantile regressions

Yao

2016

Computational Statistics & Data Analysis

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A semi-parametric mixture of quantile regressions model is proposed to allow regressions of the conditional quantiles, such as the median, on the covariates without any parametric assumption on the error densities. The median as a measure of center is known to be more robust to skewness and outliers than the mean. Modeling the quantiles instead of the mean not only improves the robustness of the model but also reveals a fuller picture of the data by fitting varying quantile functions. The proposed semi-parametric mixture of quantile regressions model is proven to be identifiable under certain weak conditions. A kernel density based EM-type algorithm is developed to estimate the model parameters, while a stochastic version of the EM-type algorithm is constructed for the variance estimation. A couple of simulation studies and several real data applications are conducted to show the effectiveness of the proposed model.

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Model-based clustering via linear cluster-weighted models

Cited by 83 publications

References 33 publications

Model-Based Clustering

Model-Based Clustering

Erratum to: The Generalized Linear Mixed Cluster-Weighted Model

Mixtures of quantile regressions

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