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Topological Analysis of Recurrent Systems
Jozef Stefan Institute. (AI Laboratory)
Pomona College. (Department of Mathematics)
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0001-6322-7542
2012 (English)Conference paper, Published paper (Refereed)
Abstract [en]

We propose a new framework for the experimental study of periodic, quasi- periodic and recurrent dynamical systems. These behaviors express themselves as topological features which we detect using persistent cohomology. The result- ing 1-cocycles yield circle-valued coordinates associated to the recurrent behavior. We demonstrate how to use these coordinates to perform fundamental tasks like period recovery and parameter choice for delay embeddings. 

Place, publisher, year, edition, pages
2012. 1-5 p.
Keyword [en]
applied algebraic topology, persistent cohomology, circle-valued coordinates, recurrent systems, periodic systems
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-107210OAI: oai:DiVA.org:kth-107210DiVA: diva2:575329
Conference
NIPS 2012 Workshop on Algebraic Topology and Machine Learning, December 8th, Lake Tahoe, Nevada
Projects
TOPOSYS
Funder
EU, FP7, Seventh Framework Programme, FP7-ICT-318493-STREP
Note

QC 20121221

Available from: 2012-12-21 Created: 2012-12-10 Last updated: 2015-01-20Bibliographically approved

Open Access in DiVA

fulltext(469 kB)257 downloads
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Type fulltextMimetype application/pdf

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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