Non-Gaussian Mixtures for Dimension Reduction, Clustering, Classification, and Discriminant Analysis
Katherine Morris, Paul D. McNicholas · arXiv (Cornell University) · 2013
We introduce a method for dimension reduction with clustering, classification, or discriminant analysis. This mixture model-based approach is based on fitting general-ized 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 ro-bust 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 three 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 re-sults to three special and limiting cases. We also compare with well several established techniques. Across all comparisons, our approach performs remarkably well.