A mixture of generalized hyperbolic factor analyzers

Tortora, Cristina; McNicholas, Paul D.; Browne, Ryan P.

doi:10.1007/s11634-015-0204-z

Cited by 44 publications

(32 citation statements)

References 62 publications

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“…It is worth noting that the MJGHD proposed herein does not need to numerically invert covariance matrices, which often fails for singularity reasons. We compare this with the parsimonious Gaussian mixture models (PGMMs) from the R package pgmm (McNicholas et al ) and the mixture of generalized hyperbolic factor analysers (MGHFAs; Tortora et al, ) from the R package mixGHD (Tortora et al ) in our real‐data applications.…”

Section: A Mixture Of Joint Generalized Hyperbolic Distributions For mentioning

confidence: 99%

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Flexible clustering of high‐dimensional data via mixtures of joint generalized hyperbolic distributions

Tang

Browne

McNicholas

2018

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A mixture of joint generalized hyperbolic distributions (MJGHD) is introduced for asymmetric clustering for highdimensional data. The MJGHD approach takes into account the cluster-specific subspaces, thereby limiting the number of parameters to estimate while also facilitating visualization of results. Identifiability is discussed, and a multi-cycle expectation-conditional maximization algorithm is outlined for parameter estimation. The MJGHD approach is illustrated on two real data sets, where the Bayesian information criterion is used for model selection.

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Section: A Mixture Of Joint Generalized Hyperbolic Distributions For mentioning

confidence: 99%

“…Browne & McNicholas, ; Lin et al, ). Dimensionality reduction approaches based on non‐elliptical distributions have received relatively little attention, and recent work includes Morris & McNicholas (), Murray et al (), Tortora et al () and Lin et al (). Each of these methods works well with particular types of data sets.…”

Section: Introductionmentioning

confidence: 99%

Flexible clustering of high‐dimensional data via mixtures of joint generalized hyperbolic distributions

Tang

Browne

McNicholas

2018

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“…Following this approach, Tortora, McNicholas, and Browne (2015) arrive at a mixture of generalized hyperbolic factor analyzers model. In doing so, they follow the same approach used by Murray et al (2014a), who develop a mixture of skew-t factor analyzers; the principal difference is the distribution of W , which is inverse gamma in the case of the skew-t distribution.…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

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172

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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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“…Due to the flexibility of the GH family, recent interest has focused on applications for mixture models and factor analysis Tortora et al, 2013). For mixture model applications, semi-parametric or non-parametric approaches can also be used.…”

Section: Introductionmentioning

confidence: 99%

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

Wraith

Forbes

2015

Computational Statistics & Data Analysis

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International audienceThe family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape

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A mixture of generalized hyperbolic factor analyzers

Cited by 44 publications

References 62 publications

Flexible clustering of high‐dimensional data via mixtures of joint generalized hyperbolic distributions

Flexible clustering of high‐dimensional data via mixtures of joint generalized hyperbolic distributions

Model-Based Clustering

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

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