<b>teigen</b>: An <i>R</i> Package for Model-Based Clustering and Classification via the Multivariate t Distribution

Andrews, Jeffrey L.; Wickins, Jaymeson R.; Boers, Nicholas M.; McNicholas, Paul D.

doi:10.18637/jss.v083.i07

Cited by 53 publications

(33 citation statements)

References 19 publications

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“…">2.Mixture of t distributions ( t M = t mixture; Andrews and McNicholas, ). The teigen() function of the teigen package (Andrews et al., ) for R is used to fit the unconstrained t mixture (corresponding to the UUUU model with respect to the nomenclature of the teigen package). The teigen() function implements the ECM algorithm described, for example, in (Andrews et al., ).…”

Section: Simulation Study: Comparison Between Mixtures That Handle MImentioning

confidence: 99%

“…The teigen() function of the teigen package (Andrews et al., ) for R is used to fit the unconstrained t mixture (corresponding to the UUUU model with respect to the nomenclature of the teigen package). The teigen() function implements the ECM algorithm described, for example, in (Andrews et al., ). Degrees of freedom are estimated and they are allowed to vary across groups. …”

Section: Simulation Study: Comparison Between Mixtures That Handle MImentioning

confidence: 99%

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Parsimonious mixtures of multivariate contaminated normal distributions

Punzo

McNicholas

2016

Biometrical J

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A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large-scale simulation study, the behavior of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.

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Section: Simulation Study: Comparison Between Mixtures That Handle MImentioning

confidence: 99%

Section: Simulation Study: Comparison Between Mixtures That Handle MImentioning

confidence: 99%

Parsimonious mixtures of multivariate contaminated normal distributions

Punzo

McNicholas

2016

Biometrical J

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“…MNMs are fitted via the gpcm() function of the R‐package mixture (Browne, ElSherbiny, & McNicholas, ), M t Ms are fitted via the teigen() function of the R‐package teigen (Andrews & McNicholas, ), MCNMs are fitted via the CNmixt() function of the R‐package ContaminatedMixt (Punzo, Mazza, & McNicholas, ), MPEMs are fitted via the mpe() function of an R package available at http://onlinelibrary.wiley.com/doi/10.1111/biom.12351/suppinfo Dang et al (Dang, Browne, & McNicholas, ), whereas a specific R code, available as Supplementary Material for Review, has been implemented to fit MLNMs. To allow for a direct comparison of the competing models, all the algorithms are initialized by providing the initial quantities

λ z_{i}^{false(0 false)}

i = 1, \dots, n

: nine times using a random initialization and once with a k ‐means initialization (as implemented by the kmeans() function for R).…”

Section: Resultsmentioning

confidence: 99%

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

2016

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This article proposes the elliptical multivariate leptokurtic‐normal (MLN) distribution to fit data with excess kurtosis. The MLN distribution is a multivariate Gram–Charlier expansion of the multivariate normal (MN) distribution and has a closed‐form representation characterized by one additional parameter denoting the excess kurtosis. It is obtained from the elliptical representation of the MN distribution, by reshaping its generating variate with the associated orthogonal polynomials. The strength of this approach for obtaining the MLN distribution lies in its general applicability as it can be applied to any multivariate elliptical law to get a suitable distribution to fit data. Maximum likelihood is discussed as a parameter estimation technique for the MLN distribution. Mixtures of MLN distributions are also proposed for robust model‐based clustering. An EM algorithm is presented to obtain estimates of the mixture parameters. Benchmark real data are used to show the usefulness of mixtures of MLN distributions. The Canadian Journal of Statistics 45: 95–119; 2017 © 2016 Statistical Society of Canada

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“…Our model can be extended beyond supervised learning to mixture model-based clustering and can be made to accommodate more specialized covariance structures such as those described in [31] and [32]. It may also be readily extended to cases with incomplete records.…”

Section: Discussionmentioning

confidence: 99%

Classification With the Matrix-Variate-t Distribution

Thompson

Maitra

Meeker

et al. 2020

Journal of Computational and Graphical Statistics

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Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-variate t-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or the classification of functional Magnetic Resonance, satellite or hand gestures images.

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teigen: An R Package for Model-Based Clustering and Classification via the Multivariate t Distribution

Cited by 53 publications

References 19 publications

Parsimonious mixtures of multivariate contaminated normal distributions

Parsimonious mixtures of multivariate contaminated normal distributions

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

Classification With the Matrix-Variate-t Distribution

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