Sampling and Limit Theories for Graph Signal Processing and Large Simplicial Complexes

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dc.contributor.advisorSegarra, Santiagoen_US
dc.creatorRoddenberry, T. Mitchellen_US
dc.date.accessioned2023-08-09T15:25:35Zen_US
dc.date.created2023-05en_US
dc.date.issued2023-03-31en_US
dc.date.submittedMay 2023en_US
dc.date.updated2023-08-09T15:25:35Zen_US
dc.description.abstractThis thesis considers the role of locality and sampling in graph signal processing and network science. In light of the prevalence of extremely large and complex network datasets, it is a timely problem to consider how the study of these objects can be reduced to the study of a distribution of simpler objects. Indeed, many methods in graph signal processing and machine learning on graphs can be described strictly in light of local graph substructures. The approach taken to this problem starts with defining the notion of taking a sample from a network, and then builds this out to a probabilistic framework for network theory. This framework is applied to understand questions of graph parameter estimation, fundamentals of graph signal processing and Fourier analysis on graphs, transferability of machine learning and signal processing methods for network data, and finally to construct meaningful limiting objects of graphs and simplicial complexes. The study undertaken in this thesis both enhances the understanding of current methods, as well as inspires new methods in light of the notions of transferability defined by sampling.en_US
dc.embargo.lift2023-11-01en_US
dc.embargo.terms2023-11-01en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationRoddenberry, T. Mitchell. "Sampling and Limit Theories for Graph Signal Processing and Large Simplicial Complexes." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115097">https://hdl.handle.net/1911/115097</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/115097en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectGraph limit theoryen_US
dc.subjectnetwork scienceen_US
dc.subjectgraph signal processingen_US
dc.titleSampling and Limit Theories for Graph Signal Processing and Large Simplicial Complexesen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical and Computer Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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