Hyperbolic Distributions and Transformations for Clustering Incomplete Data with Extensions to Matrix Variate Normality

Abstract

Under realistic scenarios, data are often incomplete, asymmetric, or of high-dimensionality. More intricate data structures often render standard approaches infeasible due to methodological or computational limitations. This monograph consists of four contributions each solving a specific problem within model-based clustering. An R package is developed consisting of a three-phase imputation method for both elliptical and hyperbolic parsimonious models. A novel stochastic technique is employed to speed up computations for hyperbolic distributions demonstrating superior performance overall. A hyperbolic transformation model is conceived for clustering asymmetrical data within a heterogeneous context. Finally, for high-dimensionality, a framework is developed for assessing matrix variate normality within three-way datasets. All things considered, this work constitutes a powerful set of tools to deal with the ever-growing complexity of big data