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Graph Nodal Domains and Data.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Graph Nodal Domains and Data./
作者:	Hamilton, Wesley A.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	92 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28418946
ISBN:	9798516058431

Graph Nodal Domains and Data.
Hamilton, Wesley A.

Graph Nodal Domains and Data. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 92 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2021.

This item must not be sold to any third party vendors.

This thesis proposes and develops a graph spectral flow for computing nodal counts and nodal deficiencies of graph Laplacian eigenvectors. Background on Laplace eigenfunctions and their nodal domains, as well as the corresponding results in the spectral graph theory literature, is given. We also review some effective tools that adapt spectral methods for the analysis of data, in particular the use of ratio cuts for partitioning and diffusion maps for dimensionality reduction. We then define two versions of the graph spectral flow and develop properties of each, after which examples of the spectral flow on a number of graphs are provided. Finally we mention ongoing lines of research related to both theoretical and applied aspects of graphs' nodal counts.

ISBN: 9798516058431Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Data

Graph Nodal Domains and Data.
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245 1 0 $a Graph Nodal Domains and Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 92 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Marzuola, Jeremy L.
502 $a Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis proposes and develops a graph spectral flow for computing nodal counts and nodal deficiencies of graph Laplacian eigenvectors. Background on Laplace eigenfunctions and their nodal domains, as well as the corresponding results in the spectral graph theory literature, is given. We also review some effective tools that adapt spectral methods for the analysis of data, in particular the use of ratio cuts for partitioning and diffusion maps for dimensionality reduction. We then define two versions of the graph spectral flow and develop properties of each, after which examples of the spectral flow on a number of graphs are provided. Finally we mention ongoing lines of research related to both theoretical and applied aspects of graphs' nodal counts.
590 $a School code: 0153.
650 4 $a Mathematics. $3 515831
650 4 $a Statistics. $3 517247
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Information science. $3 554358
653 $a Data
653 $a Eigenfunctions
653 $a Laplacian
653 $a Spectral graph theory
690 $a 0405
690 $a 0463
690 $a 0642
690 $a 0723
710 2 $a The University of North Carolina at Chapel Hill. $b Mathematics. $3 1265876
773 0 $t Dissertations Abstracts International $g 82-12B.
790 $a 0153
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28418946