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Date of Award

Fall 2012

Degree Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics and Statistics

Supervisor

Joseph Beyene

Language

English

Committee Member

Jemila Hamid, Roman Viveros-Aguilera

Abstract

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 millions of genetic variables (p) with only a limited number of study participants (n). Determining the important features proves statistically difficult, 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 but have not been tested in comparative detail. Methods: Performances of three Sparse PCA methods were evaluated through simulations. Data was generated for 56 different data-structures, ranging p, the number of underlying groups and the variance structure within them. Estimation and interpretability of the principal components (PCs) were rigorously tested. Sparse PCA methods were also applied to a real gene expression dataset. Results: All Sparse PCA methods showed improvements upon classical PCA. Some methods were best at obtaining an accurate leading PC only, whereas others were better for subsequent PCs. There exist different optimal choices of Sparse PCA methods when ranging within-group correlation and across-group variances; thankfully, one method repeatedly worked well under the most difficult scenarios. When applying methods to real data, concise groups of gene expressions were detected with the most sparse methods. Conclusions: Sparse PCA methods provide a new insightful way to detect important features amidst complex high-dimension data.

McMaster University Library

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