DOI
https://doi.org/10.25772/W6AJ-JH77
Defense Date
2011
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
J. Paul Brooks
Abstract
Principal component analysis (PCA) is a dimensionality reduction tool which captures the features of data set in low dimensional subspace. Traditional PCA uses L2-PCA and has much desired orthogonality properties, but is sensitive to outliers. PCA using L1 norm has been proposed as an alternative to counter the effect of outliers. The R environment for statistical computing already provides L2-PCA function prcomp(), but there are not many options for L1 norm PCA methods. The goal of the research was to create one R package with different options of PCA methods using L1 norm. So, we choose three different L1-PCA algorithms: PCA-L1 proposed by Kwak [10], L1-PCA* by Brooks et. al. [1], and L1-PCA by Ke and Kanade [9]; to create a package pcaL1 in R, interfacing with C implementation of these algorithms. An open source software for solving linear problems, CLP, is used to solve the optimization problems for L1-PCA* and L1-PCA. We use this package on human microbiome data to investigate the relationship between people based on colonizing bacteria.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
May 2011