Repository logo
 

Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman iterative techniques

Simple item page
dc.contributor.authorRohrbacker, Nicholas, author
dc.contributor.authorKirby, Michael, advisor
dc.contributor.authorPeterson, Christopher, committee member
dc.contributor.authorLiu, Jiangguo, committee member
dc.contributor.authorBen-Hur, Asa, committee member
dc.date.accessioned2007-01-03T08:26:24Z
dc.date.available2007-01-03T08:26:24Z
dc.date.issued2012
dc.description.abstractIn this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular Value Decomposition (BSSVD) and Bisparse Singular Value Decomposition with an ℓ1-constrained classifier BSSVDℓ1. For each of these problems we construct and solve a new optimization problem using these Bregman iterative techniques. Each of the proposed optimization problems contain one or more ℓ1-regularization terms to enforce sparsity in the solutions. The use of the ℓ1-norm to enforce sparsity is a widely used technique, however, its lack of differentiability makes it more difficult to solve problems including these types of terms. Bregman iterations make these solutions possible without the addition of variables and algorithms such as the Split Bregman algorithm makes additional penalty terms and multiple ℓ1 terms feasible, a trait that is not present in other state of the art algorithms such as the fixed point continuation algorithm. It is also shown empirically to be faster than another iterative solver for total variation image denoising, another ℓ1-regularized problem, in. We also link sparse Principal Components to cluster centers, denoise Hyperspectral Images using the BSSVD, identify and remove ambiguous observations from a classification problem using the algorithm and detect anomalistic subgraphs using Sparse Eigenvectors of the Modularity Matrix.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierRohrbacker_colostate_0053A_11527.pdf
dc.identifierETDF2012500322MATH
dc.identifier.urihttp://hdl.handle.net/10217/71581
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectconvex optimization
dc.subjectmodularity
dc.subjectsparse PCA
dc.subjectbisparse singular value cecomposition
dc.subjectSplit Bregman
dc.subjectsupport vector machine
dc.titleSparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman iterative techniques
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Rohrbacker_colostate_0053A_11527.pdf
Size:
3.35 MB
Format:
Adobe Portable Document Format
Description:
Download

Collections

2000-2019
Theses and Dissertations