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

Abstract

The MixGHD package for R performs model-based clustering, classification, and discriminant analysis using the generalized hyperbolic distribution (GHD). This approach is suitable for data that can be considered a realization of a (multivariate) continuous random variable. The GHD has the advantage of being flexible due to skewness, concentration, and index parameters; as such, clustering methods that use this distribution are capable of estimating clusters characterized by different shapes. The package provides five different models all based on the GHD, an efficient routine for discriminant analysis, and a function to measure cluster agreement. This paper is split into three parts: the first is devoted to the formulation of each method, extending them for classification and discriminant analysis applications, the second focuses on the algorithms, and the third shows the use of the package on real datasets.

A Bayesian approach for clustering skewed data using mixtures of multivariate normal-inverse Gaussian distributions

“…Hence, mixtures of generalized hyperbolic distributions (MixGHD; Browne and McNicholas, 2015) implemented in the R package MixGHD (Tortora et al, 2018) are also applied to these datasets. Mixtures of generalized hyperbolic distributions (McNeil et al, 2015) also have the flexibility of modeling skewed as well as symmetric components.…”

Flexible Clustering with a Sparse Mixture of Generalized Hyperbolic Distributions

“…4.2) is designed to assess the proposed sparse modelling approach through different dependency patterns among variables for each component. We compare our proposed model with the parsimonious Gaussian mixture models (PGMM; McNicholas and Murphy, 2008) from R package pgmm (McNicholas et al, 2011) , the mixture of canonical fundamental skewt distributions (FM-CFUST; Lee and McLachlan, 2016) from R package EMMIXcskew (Lee and McLachlan, 2015), the mixture of generalized hyperbolic distributions (MGHD; Browne and McNicholas, 2015) and the mixture of generalized hyperbolic factor analyzers (MGHFA; Tortora et al, 2016) from R package mixGHD (Tortora et al, 2017) in Sect. 4.3 (Experiment 3).…”

Model-based clustering and classification using mixtures of multivariate skewed power exponential distributions

“…We compared the performance of the MSPE mixture models with mixture model implementations based on the MPE distribution (Dang et al, 2015), the generalized hyperbolic distribution (MixGHD; Tortora et al, 2018), and the Gaussian distribution (mixture; Browne et al, 2018). We chose these mixtures for comparison as Gaussian mixtures remains widely used and the generalized hyperbolic distribution has special cases that include parameterizations of inverse Gaussian, variance gamma, skew-t, multivariate normal-inverse Gaussian, and asymmetric Laplace distribution.…”

“…The Swiss banknote dataset (Tortora et al, 2018) looked at 6 different measurements from 100 genuine and 100 counterfeit banknotes. The measurements were length, width of the right and left edges, the top and bottom margin widths and the length of the diagonal.…”

“…Bankruptcy Dataset The bankruptcy dataset (Tortora et al, 2018) looked at the ratio of retained earnings to total assets, and the ratio of earnings before interests and taxes to total assets of 33 financially sound and 33 bankrupt American firms.…”