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Mixtures of Shifted AsymmetricLaplace Distributions
June 2014 (vol. 36 no. 6)
pp. 1149-1157
Paul D. McNicholas, Department of Mathematics & Statistics, University of Guelph, Guelph, Canada
Ryan P. Browne, Department of Mathematics & Statistics, University of Guelph, Guelph, Canada
Brian C. Franczak, Department of Mathematics & Statistics, University of Guelph, Guelph, Canada
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the generalized inverse Gaussian distribution. This approach is mathematically elegant and relatively computationally straightforward. Our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications. In these analyses, our mixture of shifted asymmetric Laplace distributions performs favourably when compared to the popular Gaussian approach. This work, which marks an important step in the non-Gaussian model-based clustering and classification direction, concludes with discussion as well as suggestions for future work.
Index Terms:
Algorithm design and analysis,Annealing,Mathematical model,Convergence,Gaussian distribution,Indexes,Random variables,multivariate statistics,Statistical computing
Citation:
Paul D. McNicholas, Ryan P. Browne, Brian C. Franczak, "Mixtures of Shifted AsymmetricLaplace Distributions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 6, pp. 1149-1157, June 2014, doi:10.1109/TPAMI.2013.216
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