| This thesis is concerned with parametric classification of non-standard data. Specifically, methods are developed for classifying two of the most common types of non-Gaussian distributed data: data with mixed categorical and continuous variables (often called mixed-mode data), and sparse count data. Both supervised and unsupervised methods are described. First, a promising, recently proposed method that uses finite mixtures of homogeneous conditional Gaussian distributions (Lawrence and Krzanowski, 1996) is shown to be non-identifiable. Identifiable finite mixtures of homogeneous conditional Gaussian distributions are obtained by imposing constraints on some of the model parameters. Then, in contrast, it is shown that supervised classification of mixed-mode data using the homogeneous conditional Gaussian model can sometimes be improved by relaxing parameter constraints in the model; specifically, certain features of the continuous variable covariance matrix---such as volume, shape or orientation---are allowed to differ between groups. In addition, the use of latent class and latent profile models in supervised mixed-mode classification is investigated. Finally, mixtures of over-dispersed Poisson latent variable models are developed for unsupervised classification of sparse count data. Simulation studies suggest that for non-Gaussian data these methods can significantly outperform methods based in Gaussian theory. |
