Mixtures of Multivariate Power Exponential Distributions

Abstract

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of the scale matrix. A generalized expectation-maximization algorithm is presented that combines convex optimization via a minorization-maximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.

References in corpus (7)

• Natural Scales in Geographical Patterns
• A Mixture of Generalized Hyperbolic Distributions
• Mixtures of Shifted Asymmetric Laplace Distributions
• Parameter Estimation For Multivariate Generalized Gaussian Distributions
• Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models
• Variational Bayes Approximations for Clustering via Mixtures of Normal Inverse Gaussian Distributions
• Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models