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Unsupervised Learning via Mixtures of Skewed Distributions with Hypercube Contours

Authors
  • Franczak, Brian C.
  • Tortora, Cristina
  • Browne, Ryan P.
  • McNicholas, Paul D.
Type
Preprint
Publication Date
Sep 17, 2014
Submission Date
Mar 10, 2014
Identifiers
DOI: 10.1016/j.patrec.2015.02.011
Source
arXiv
License
Yellow
External links

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.

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