Clustering, Classification, Discriminant Analysis, and Dimension Reduction via Generalized Hyperbolic Mixtures

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of model-based clustering, classification, or discriminant analysis. A reduced subspace of the data is derived by considering the extent to which group means and group covariances vary. The members of the subspace arise through linear combinations of the original data, and are ordered by importance via the associated eigenvalues. The observations can be projected onto the subspace, resulting in a set of variables that captures most of the clustering information available. The use of generalized hyperbolic mixtures gives a robust framework capable of dealing with skewed clusters. Although dimension reduction is increasingly in demand across many application areas, the authors are most familiar with biological applications and so two of the five real data examples are within that sphere. Simulated data are also used for illustration. The approach introduced herein can be considered the most general such approach available, and so we compare results to three special and limiting cases. Comparisons with several well established techniques illustrate its promising performance.