Mixtures of Shifted Asymmetric Laplace Distributions
This work provides a non-Gaussian alternative for model-based clustering and classification, though it appears incremental as it builds on existing mixture modeling approaches.
The authors tackled the problem of clustering and classification by introducing a mixture of shifted asymmetric Laplace distributions, which performed favorably compared to Gaussian methods in analyses on simulated and real data.
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 general 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.