Mixtures of Shifted Asymmetric Laplace Distributions

TL;DR

This paper introduces a novel mixture model based on shifted asymmetric Laplace distributions for clustering and classification, demonstrating its effectiveness over Gaussian models through simulations and real data analysis.

Contribution

It develops a new mixture modeling approach using shifted asymmetric Laplace distributions and a variant of the EM algorithm for efficient parameter estimation.

Findings

Performs favorably compared to Gaussian models

Effective on both simulated and real datasets

Provides a mathematically elegant and computationally straightforward method

Abstract

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.