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Algorithms and geometric analysis of data sets that are invariant under a group action

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dc.contributor.authorSmith, Elin Rose, author
dc.contributor.authorPeterson, Christopher Scott, 1963-, advisor
dc.contributor.authorBates, Daniel J. (Daniel James), 1979-, committee member
dc.contributor.authorKirby, Michael, 1961-, committee member
dc.contributor.authorMcConnell, Ross M., committee member
dc.date.accessioned2007-01-03T04:51:02Z
dc.date.available2007-01-03T04:51:02Z
dc.date.issued2010
dc.description.abstractWe apply and develop pattern analysis techniques in the setting of data sets that are invariant under a group action. We apply Principal Component Analysis to data sets of images of a rotating object in Chapter 5 as a means of obtaining visual and low-dimensional representations of data. In Chapter 6, we propose an algorithm for finding distributions of points in a base space that are (locally) optimal in the sense that subspaces in the associated data bundle are distributed with locally maximal distance between neighbors. In Chapter 7, we define a distortion function that measures the quality of an approximation of a vector bundle by a set of points. We then use this function to compare the behavior of four standard distance metrics and one non-metric. Finally, in Chapter 8, we develop an algorithm to find the approximate intersection of two data sets.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierSmith_colostate_0053A_10101.pdf
dc.identifierETDF2010100006MATH
dc.identifier.urihttp://hdl.handle.net/10217/44768
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.subjectprincipal component analysis
dc.subjectpattern analysis
dc.subjectminimal energy configuration
dc.subjectimage analysis
dc.subjectgroup actions
dc.subjectdata bundle
dc.subjectGeometric group theory
dc.subjectGeometric analysis
dc.subjectInvariant measures
dc.subjectCluster analysis
dc.subjectPattern perception
dc.titleAlgorithms and geometric analysis of data sets that are invariant under a group action
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.)

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