Singular Value Decomposition for High Dimensional Data

Loading...
Thumbnail Image
Degree type
Doctor of Philosophy (PhD)
Graduate group
Statistics
Discipline
Subject
Cross validation
Denoise
Low rank matrix approximation
PCA
Penalization
Thresholding
Statistics and Probability
Funder
Grant number
License
Copyright date
2014-08-19T00:00:00-07:00
Distributor
Related resources
Author
Contributor
Abstract

Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. We suppose the true singular vectors have sparse representations in a certain basis. We propose an iterative thresholding algorithm that can estimate the subspaces spanned by leading left and right singular vectors and also the true mean matrix optimally under Gaussian assumption. We further turn the algorithm into a practical methodology that is fast, data-driven and robust to heavy-tailed noises. Simulations and a real data example further show its competitive performance. The dissertation contains two chapters. For the ease of the delivery, Chapter 1 is dedicated to the description and the study of the practical methodology and Chapter 2 states and proves the theoretical property of the algorithm under Gaussian noise.

Advisor
Andreas Buja
Zongming Ma
Date of degree
2012-01-01
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation