kth.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
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
  • text
  • asciidoc
  • rtf
Using topology and signature methods to study spatiotemporal data with machine learning
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2023 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Att studera spatiotemporal data genom topologi, vägsignaturer och maskininlärning (Swedish)
Abstract [en]

This thesis explores a new way to analyze spatiotemporal data. By combining topology, the path signature and machine learning a robust model to analyze swarming behavior over time is created. Using persistent homology a representation of spatial data is obtained and the path signature gives us a representation for how this changes over time. This representation allows us to compare samples even if they have different amounts of time steps and different length of the sequence. It is also resistant to noise in the spatial representation. Using this data is then used to train a gaussian process regressor to extract parameters that govern the movement of swarms. Our analysis shows that the tested method is a good candidate for analyzing spatiotemporal data and that it warrants further studies.

Abstract [sv]

Detta examensarbete utforskar ett nytt sätt att analysera spatiotemporal data. Genom att kombinera topologi, vägsignaturer och maskininlärning skapas en robust modell för att analysera svärmar beter sig över tid. Genom persistent homology erhålls en representation av spatial data och dess vägsignatur ger oss en representation för hur detta förändras över tiden. Denna representation gör det möjligt för oss att jämföra data även om de har olika antal tidssteg och sekvenserna är olika långa. Den är också motståndskraftig mot brus i den spatiala representationen. Denna data används sedan för att träna en gaussisk process-regressor för att extrahera parametrar som styr svärmarnas rörelse. Vår analys visar att den testade metoden är en bra kandidat för att analysera spatiotemporal data och att den är värd att studera ytterligare.

Place, publisher, year, edition, pages
2023. , p. 43
Series
TRITA-SCI-GRU ; 2023:469
Keywords [en]
Topology, Persistent homology, Path signature, Gaussian process, temporospatial data, TDA, topologisk dataanalys, applied mathematics, mathematics
Keywords [sv]
Topologi, persistent homologi, vägsignatur, Gaussisk process, temporospatiala data, TDA, topologisk dataanalys, tillämpad matematik, matematik
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-346701OAI: oai:DiVA.org:kth-346701DiVA, id: diva2:1859953
External cooperation
École Polytechnique Fédérale de Lausanne
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2024-05-23 Created: 2024-05-23 Last updated: 2024-05-23Bibliographically approved

Open Access in DiVA

fulltext(1289 kB)22 downloads
File information
File name FULLTEXT01.pdfFile size 1289 kBChecksum SHA-512
2ba627c7593ac1cd302321961484fc343c3fa23df07c2568e71eb3a3425e900210614a34070ba2365c9f15998b4adcb1232ae3041429bfe2e6f448c48eb9a88c
Type fulltextMimetype application/pdf

By organisation
Mathematics (Div.)
Other Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 22 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 124 hits
CiteExportLink to record
Permanent link

Direct link
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
  • text
  • asciidoc
  • rtf