Extensions to the OCLUST Algorithm

Abstract

OCLUST is a clustering algorithm that trims outliers in Gaussian mixture models. While mixtures of multivariate Gaussian distributions are a useful way to model heterogeneity in data, it is not always an appropriate assumption that the data arise from a finite mixture of Gaussian distributions. This thesis extends the OCLUST algorithm to three types of data which depart from the multivariate Gaussian distribution. The first extension, called funOCLUST, is developed for data which exist in functional form. Next, MVN-OCLUST applies outlier trimming to matrix-variate normal data. Finally, the skewOCLUST algorithm is formulated for skewed data by applying a transformation to normality. However, this final extension occurs after a brief detour in Chapter 5 to establish a foundation for the final chapter.