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Grassmann, Flag, and Schubert varieties in applications

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dc.contributor.authorMarrinan, Timothy P., author
dc.contributor.authorKirby, Michael, advisor
dc.contributor.authorPeterson, Chris, advisor
dc.contributor.authorAzimi-Sadjadi, Mahmood R., committee member
dc.contributor.authorBates, Dan, committee member
dc.contributor.authorDraper, Bruce, committee member
dc.date.accessioned2017-06-09T15:42:54Z
dc.date.available2018-06-06T22:59:22Z
dc.date.issued2017
dc.description.abstractThis dissertation develops mathematical tools for signal processing and pattern recognition tasks where data with the same identity is assumed to vary linearly. We build on the growing canon of techniques for analyzing and optimizing over data on Grassmann manifolds. Specifically we expand on a recently developed method referred to as the flag mean that finds an average representation for a collection data that consists of linear subspaces of possibly different dimensions. When prior knowledge exists about relationships between these data, we show that a point analogous to the flag mean can be found as an element of a Schubert variety to incorporates this theoretical information. This domain restriction relates closely to a recent result regarding point-to-set functions. This restricted average along with a property of the flag mean that prioritizes weak but common information, leads to practical applications of the flag mean such as chemical plume detection in long-wave infrared hyperspectral videos, and a modification of the well-known diffusion map for adaptively visualizing data relationships in 2-dimensions.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierMarrinan_colostate_0053A_14161.pdf
dc.identifier.urihttp://hdl.handle.net/10217/181430
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.subjectpattern analysis
dc.subjectsingular value decomposition
dc.subjecthyperspectral images
dc.subject.lcshGrassmann manifolds
dc.subject.lcshFlag manifolds
dc.subject.lcshSchubert varieties
dc.titleGrassmann, Flag, and Schubert varieties in applications
dc.typeText
dcterms.embargo.expires2018-06-06
dcterms.embargo.terms2018-06-06
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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