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Alex_Elchesen_Masters_Thesis.pdf (747.81 KB)
ETD Abstract Container
Abstract Header
Stability of Zigzag Persistence with Respect to a Reflection-type Distance
Author Info
Elchesen, Alex
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707343134983
Abstract Details
Year and Degree
2017, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Abstract
We use the reflection functors introduced by Bernstein, Gelfand, and Ponomarev to define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the bottleneck distance between the persistence diagrams of the given modules. We also extend our distance to weighted zigzag modules and prove an analogous result in this setting.
Committee
Facundo Mémoli, Dr. (Advisor)
Matthew Kahle, Dr. (Committee Member)
Pages
90 p.
Subject Headings
Mathematics
Keywords
Zigzag persistence
;
zigzag modules
;
reflection functors
;
stability
;
persistent homology
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Citations
Elchesen, A. (2017).
Stability of Zigzag Persistence with Respect to a Reflection-type Distance
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707343134983
APA Style (7th edition)
Elchesen, Alex.
Stability of Zigzag Persistence with Respect to a Reflection-type Distance.
2017. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707343134983.
MLA Style (8th edition)
Elchesen, Alex. "Stability of Zigzag Persistence with Respect to a Reflection-type Distance." Master's thesis, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707343134983
Chicago Manual of Style (17th edition)
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Document number:
osu1492707343134983
Download Count:
570
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.