Unsupervised Learning via Mixtures of Skewed Distributions with Hypercube Contours

Abstract

Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have two unique features: they include a multivariate weight function, and the marginal distributions are also asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could equally well be used in the supervised or semi-supervised paradigms. The expectation-maximization algorithm is used for parameter estimation and the Bayesian information criterion is used for model selection. Simulated and real data sets are used to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components.

References in corpus (7)

• Natural Scales in Geographical Patterns
• Simultaneous model-based clustering and visualization in the Fisher discriminative subspace
• Parsimonious Skew Mixture Models for Model-Based Clustering and Classification
• Estimating Common Principal Components in High Dimensions
• Dimension reduction for model-based clustering
• Mixtures of Variance-Gamma Distributions
• Parsimonious Shifted Asymmetric Laplace Mixtures

Cited by in corpus (2)

• Clustering, Classification, Discriminant Analysis, and Dimension Reduction via Generalized Hyperbolic Mixtures
• Mixtures of Generalized Hyperbolic Distributions and Mixtures of Skew-t Distributions for Model-Based Clustering with Incomplete Data