A matrix variate skew‐<i>t</i> distribution

Gallaugher, Michael P. B.; McNicholas, Paul D.

doi:10.1002/sta4.143

Cited by 35 publications

(25 citation statements)

References 43 publications

(57 reference statements)

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“…The matrix variate normal distribution is related to the multivariate normal distribution, as discussed in Harrar & Gupta (2008) More recently, Gallaugher & McNicholas (2017, 2019 derived a total of four skewed matrix variate distributions using a variance mean matrix variate mixture approach. This assumes that a random matrix X can be written as…”

Section: Matrix Variate Distributionsmentioning

confidence: 99%

“…where M and A are n × p matrices representing the location and skewness, respectively, V ∼ N n×p (0, Σ, Ψ), and W > 0 is a random variable with density h(w|θ). Gallaugher & McNicholas (2017), show that the matrix variate skew-t distribution, with ν degrees of freedom, arises from (7) with W ST ∼ IGamma(ν/2, ν/2), where IGamma(·) denotes the inverse-gamma distribution with density…”

Section: Matrix Variate Distributionsmentioning

confidence: 99%

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Mixtures of skewed matrix variate bilinear factor analyzers

Gallaugher

McNicholas

2019

Adv Data Anal Classif

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Clustering is the process of finding and analyzing underlying group structure in data. In recent years, data as become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate or three way data. Furthermore, the few methods that are available all assume matrix variate normality, which is not always sensible if cluster skewness or excess kurtosis is present. Mixtures of bilinear factor analyzers models using skewed matrix variate distributions are proposed. In all, four such mixture models are presented, based on matrix variate skew-t, generalized hyperbolic, variance gamma and normal inverse Gaussian distributions, respectively.

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Section: Matrix Variate Distributionsmentioning

confidence: 99%

Section: Matrix Variate Distributionsmentioning

confidence: 99%

Mixtures of skewed matrix variate bilinear factor analyzers

Gallaugher

McNicholas

2019

Adv Data Anal Classif

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“…and Harrar and Gupta (2008). Most recently, Gallaugher and McNicholas (2017), considered a matrix variate skew-t distribution using a matrix normal variance-mean mixture.…”

Section: Background 21 the Matrix Variate Normal And Related Distribmentioning

confidence: 99%

Three skewed matrix variate distributions

Gallaugher

McNicholas

2019

Statistics & Probability Letters

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Three-way data can be conveniently modelled by using matrix variate distributions.Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix variate distributions that incorporate skewness, as well as other flexible properties such as concentration, are discussed. Equivalences to multivariate analogues are presented, and moment generating functions are derived. Maximum likelihood parameter estimation is discussed, and simulated data is used for illustration.

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“…Recently, the matrix mixture model was extended for various non-normal matrix data: Refs. [6,7] proposed finite mixture of matrix skewed distributions, and [8] introduced two matrix-variate distributions-both elliptical heavy-tailed generalizations of the matrix-variate normal distribution that are used in a finite mixture model. Ref.…”

Section: Introductionmentioning

confidence: 99%

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

Heo

Baek

2021

Entropy

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Along with advances in technology, matrix data, such as medical/industrial images, have emerged in many practical fields. These data usually have high dimensions and are not easy to cluster due to their intrinsic correlated structure among rows and columns. Most approaches convert matrix data to multi dimensional vectors and apply conventional clustering methods to them, and thus, suffer from an extreme high-dimensionality problem as well as a lack of interpretability of the correlated structure among row/column variables. Recently, a regularized model was proposed for clustering matrix-valued data by imposing a sparsity structure for the mean signal of each cluster. We extend their approach by regularizing further on the covariance to cope better with the curse of dimensionality for large size images. A penalized matrix normal mixture model with lasso-type penalty terms in both mean and covariance matrices is proposed, and then an expectation maximization algorithm is developed to estimate the parameters. The proposed method has the competence of both parsimonious modeling and reflecting the proper conditional correlation structure. The estimators are consistent, and their limiting distributions are derived. We applied the proposed method to simulated data as well as real datasets and measured its clustering performance with the clustering accuracy (ACC) and the adjusted rand index (ARI). The experiment results show that the proposed method performed better with higher ACC and ARI than those of conventional methods.

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A matrix variate skew‐t distribution

Cited by 35 publications

References 43 publications

Mixtures of skewed matrix variate bilinear factor analyzers

Mixtures of skewed matrix variate bilinear factor analyzers

Three skewed matrix variate distributions

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

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