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

Abstract

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.

A Probabilistic Distance Clustering Algorithm Using Gaussian and Student-t Multivariate Density Distributions

“…However, if the objective is dealing with outliers, it will be better to consider the PDQ approach with the multivariate contaminated normal distribution [25] and this will be a topic of future work. Other approaches for handling cluster concentration will also be considered (e.g., [9]) as will methods that accommodate asymmetric, or skewed, clusters (e.g., [18,19,21,22,32,34]). Let f (x i ; k , k ) be the generic symmetric unimodal multivariate density function of the random variable with parameter k and location parameter k then satisfies all the three properties and it is a dissimilarity measure for k = 1, … , K.…”

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

“…Until recently, the component densities have typically been Gaussian distributed, and several parsimonious extensions of Gaussian mixtures for high-dimensional data have been proposed (e.g., Ghahramani and Hinton 1997;McLachlan, Peel, and Bean 2003;Bouveyron, Girard, and Schmid 2007;Murphy 2008, 2010;Baek, McLachlan, and Flack 2010;Montanari and Viroli 2011). Recently, the focus of the literature has been on mixtures of non-Gaussian distributions for high-dimensional datasets (e.g., Andrews and McNicholas 2011a,b;Steane, McNicholas, and Yada 2012;Lin, McNicholas, and Hsiu 2014;Murray, McNicholas, and Browne 2014b;Murray, Browne, and McNicholas 2014a;Lin, McLachlan, and Lee 2016;McNicholas, McNicholas, and Browne 2017;Tang, Browne, and McNicholas 2018;Kim and Browne 2019;Murray, Browne, and McNicholas 2020;Punzo, Blostein, and McNicholas 2020). Of particular interest is the generalized hyperbolic distribution (GHD) which can detect clusters with non-elliptical form because it contains skewness, concentration, and index parameters.…”

A Mixture of Coalesced Generalized Hyperbolic Distributions

“…A little beyond the turn of the century, work on t-mixtures burgeoned into a substantial subfield of mixture model-based classification (e.g., McLachlan et al, 2007;McNicholas, 2011a,b, 2012;Baek and McLachlan, 2011;Steane et al, 2012;Lin et al, 2014;Pesevski et al, 2018). Around the same time, work on mixtures of skewed distributions took off, including work on skew-normal mixtures (e.g., Lin, 2009), skewt mixtures (e.g., Lin, 2010;McNicholas, 2012, 2014;Lee and McLachlan, 2013a,b;Murray et al, 2014), Laplace mixtures (e.g., Franczak et al, 2014), variance-gamma mixtures (McNicholas et al, 2017), generalized hyperbolic mixtures (Browne and McNicholas, 2015), and other non-elliptically contoured distributions (e.g., Karlis and Santourian, 2009;Murray et al, 2017;Tang et al, 2018). A thorough review of work on model-based clustering is given by McNicholas (2016b).…”