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Sparse Principal Component Analysis for High-Dimensional Data: A Comparative Study

Background: Through unprecedented advances in technology, high-dimensional datasets have exploded into many fields of observational research. For example, it is now common to expect thousands or sometimes millions of genetic variables (p) with only a limited number of study participants (n). Determining the important features, in whatever context, proves extremely difficult from a statistical point of view, as multivariate analysis techniques become flooded and mathematically insufficient when n < p. Principal Component Analysis (PCA) is a commonly used multivariate method for dimension reduction and data visualization but suffers from these issues. A collection of Sparse PCA methods have been proposed to counter these flaws and obtain insight to variable grouping structure but have not been tested in comparative detail. This thesis will compare three of the latest Sparse PCA methods, exposing the optimal choices under a variety of scenarios. Methods: Performances of Sparse PCA methods were evaluated through simulations. Data was generated for 56 different scenarios, ranging various properties of the variance structure from which PCA output depend on; p n , the number of underlying groups, and the variance structure between and within them. Prediction-based