Clustering with the multivariate normal inverse Gaussian distribution

O’Hagan, Adrian, Thomas Brendan Murphy, Isobel Claire Gormley, Paul D. McNicholas and Dimitris Karlis

Computational Statistics & Data Analysis, 2016, vol. 93, issue C, 18-30

Abstract: Many model-based clustering methods are based on a finite Gaussian mixture model. The Gaussian mixture model implies that the data scatter within each group is elliptically shaped. Hence non-elliptical groups are often modeled by more than one component, resulting in model over-fitting. An alternative is to use a mean–variance mixture of multivariate normal distributions with an inverse Gaussian mixing distribution (MNIG) in place of the Gaussian distribution, to yield a more flexible family of distributions. Under this model the component distributions may be skewed and have fatter tails than the Gaussian distribution. The MNIG based approach is extended to include a broad range of eigendecomposed covariance structures. Furthermore, MNIG models where the other distributional parameters are constrained is considered. The Bayesian Information Criterion is used to identify the optimal model and number of mixture components. The method is demonstrated on three sample data sets and a novel variation on the univariate Kolmogorov–Smirnov test is used to assess goodness of fit.

Keywords: Model-based clustering; Multivariate normal inverse Gaussian distribution; mclust; Information metrics; Kolmogorov–Smirnov goodness of fit (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:93:y:2016:i:c:p:18-30

DOI: 10.1016/j.csda.2014.09.006

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