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Geometric Techniques in Data Science.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric Techniques in Data Science./
Author:	Li, Binglin.
Description:	1 online resource (79 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: A.
Contained By:	Dissertations Abstracts International85-03A.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30568277click for full text (PQDT)
ISBN:	9798380162098

Geometric Techniques in Data Science.
Li, Binglin.

Geometric Techniques in Data Science. - 1 online resource (79 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: A.

Thesis (Ph.D.)--University of Georgia, 2023.

Includes bibliographical references

Geometry has been a dominating subject in mathematics and many difficult mathematical conjectures/problems have been proved via developing deep geometric techniques. One of the most famous examples is the proof of Fermat's last theorem which breaks down to studying modularity of a certain class of elliptic curves. A longstanding problem from representation theory of reductive groups was also resolved (by Ngo Bao Chau in his celebrated Fields medal work) through a careful study of the geometry of Hitchin fibrations. Such phenomena is expected in data science, where geometry is expected to reveal deep hidden structures of the data and provide magic solutions and frameworks to various statistical learning problems. In this thesis we will use compositional data analysis as a demonstrating example of geometric techniques, followed by other potential applications of other data problems.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798380162098Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Hitchin fibrationsIndex Terms--Genre/Form:

542853
Electronic books.

Geometric Techniques in Data Science.
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245 1 0 $a Geometric Techniques in Data Science.
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500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: A.
500 $a Advisor: Ahn, Jeongyoun.
502 $a Thesis (Ph.D.)--University of Georgia, 2023.
504 $a Includes bibliographical references
520 $a Geometry has been a dominating subject in mathematics and many difficult mathematical conjectures/problems have been proved via developing deep geometric techniques. One of the most famous examples is the proof of Fermat's last theorem which breaks down to studying modularity of a certain class of elliptic curves. A longstanding problem from representation theory of reductive groups was also resolved (by Ngo Bao Chau in his celebrated Fields medal work) through a careful study of the geometry of Hitchin fibrations. Such phenomena is expected in data science, where geometry is expected to reveal deep hidden structures of the data and provide magic solutions and frameworks to various statistical learning problems. In this thesis we will use compositional data analysis as a demonstrating example of geometric techniques, followed by other potential applications of other data problems.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 517247
650 4 $a Mathematics education. $3 641129
650 4 $a Applied mathematics. $3 2122814
653 $a Hitchin fibrations
653 $a Fermat's last theorem
653 $a Statistical learning problems
653 $a Compositional data analysis
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0463
690 $a 0280
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a University of Georgia. $b Statistics - PHD. $3 3682448
773 0 $t Dissertations Abstracts International $g 85-03A.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30568277 $z click for full text (PQDT)