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What and Who
Title:Improved Approximate Rips Filtrations with Shifted Integer Lattices
Speaker:Aruni Choudhary
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1
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Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 29 August 2017
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
Rips complexes are important structures for analyzing topological features of

metric spaces. Unfortunately, generating these complexes constitutes an expensive task
because of a combinatorial explosion in the complex size. For $n$ points in $\mathbb{R}^d$, we present a scheme to construct a $3\sqrt{2}$-approximation of the
multi-scale filtration of the $L_\infty$-Rips complex, which extends to a $O(d^{0.25})$-approximation of the Rips filtration for the Euclidean case. The $k$-skeleton of the resulting approximation has a total size of $n2^{O(d\log k)}$. The scheme is based on the integer lattice and on the barycentric subdivision of the $d$-cube.

Contact
Name(s):Aruni Choudhary
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Created:
Aruni Choudhary, 07/17/2017 08:40 AM
Last modified:
Uwe Brahm/MPII/DE, 08/29/2017 04:01 AM
  • Aruni Choudhary, 07/25/2017 03:29 PM
  • Aruni Choudhary, 07/17/2017 08:40 AM -- Created document.