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A Study of Isomap Extensions and Topological Data Analysis with Applications to Financial Data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
En Studie av Isomaputvidgningar samt TopologiskDataanalys med Applikationer inom Finansiell Data (Swedish)
Abstract [en]

This thesis focuses mainly on nonlinear dimensionality reduction. A comparison of a number of different extensions of the Isomap-algorithm found in the literature is presented as well as an introduction to the underlying theory. Further, two novel extensions of the algorithm are introduced. Residual variance is used as a means of quantifying performance and optimizing parameters. One of the novel approaches, NNL-Isomap, is applied to financial data sets such as the S&P 500, the results are compared with those from PCA and, when appropriate, well-known academic models. The thesis further introduces a selection of concepts from topological data analysis together with corresponding short explanatory examples as well as applies these concepts to some simple financial examples.

Abstract [sv]

Denna uppsats huvudfokus kretsar kring ickelinjär dimensionsreducering. En jämförelse av ett antal olika kända utvidgningar av Isomap-algoritmen ges, samt en introduktion till den bakomliggande teorin. Vidare presenteras två egenutvecklade utvidgningar av algoritmen. För att mäta prestanda samt optimera parametrar används residual variance-metoden. En av de egenutvecklade utvidgningarna, NNL-Isomap, appliceras på finansiella dataset såsom från S&P 500, och dess resultat jämförs med både det av PCA samt välkända akademiska modeller. Ett urval av begrepp härstammandes från topologisk dataanalys introduceras tillsammans med ett par korta exempel, dessa begrepp appliceras sedan på enklare finansiella exempel.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:13
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-243856OAI: oai:DiVA.org:kth-243856DiVA, id: diva2:1287729
External cooperation
AP3
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2019-02-11 Created: 2019-02-11 Last updated: 2019-02-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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