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A pictorial approach to persistent homology Bubenik, Peter

Description

I will present a simple-minded view of interleaving: we want two diagrams to fit together inside a bigger diagram. I will show how this idea can be used to draw pictures that prove a number of persistence results. Surprisingly (to us!) carefully working out the theory underlying these ideas led us to discover that interleaving distance and Gromov-Hausdorff distance are both special cases of a richer theory. Joint work with Vin de Silva and Jonathan Scott.

Item Metadata

Title
A pictorial approach to persistent homology
Creator
Bubenik, Peter
Publisher
Banff International Research Station for Mathematical Innovation and Discovery
Date Issued
2017-08-03T16:42
Description
I will present a simple-minded view of interleaving: we want two diagrams to fit together inside a bigger diagram. I will show how this idea can be used to draw pictures that prove a number of persistence results. Surprisingly (to us!) carefully working out the theory underlying these ideas led us to discover that interleaving distance and Gromov-Hausdorff distance are both special cases of a richer theory. Joint work with Vin de Silva and Jonathan Scott.
Extent
56 minutes
Subject
Mathematics; Algebraic topology; Probability theory and stochastic processes; Data mining
Type
Moving Image
File Format
video/mp4
Language
eng
Notes
Author affiliation: University of Florida
Series
BIRS Workshop Lecture Videos (Banff, Alta)
Date Available
2018-01-30
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0363312
URI
http://hdl.handle.net/2429/64498
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International