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Simplex-Based Dimension Estimation of Topological Manifolds
Chuo University, Japan.
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-7557-4904
Chuo University, Japan.
2016 (English)In: 2016 23RD INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR), IEEE COMPUTER SOC , 2016, p. 3609-3614Conference paper, Published paper (Refereed)
Abstract [en]

Dimension reduction is one of the most important issues in machine learning and computational intelligence. Typical data sets are point clouds in a high dimensional space with a hidden structure to be found in low dimensional submanifolds. Finding this intrinsic manifold structure is very important in the understanding of the data and for reducing computational complexity. In this paper, we propose a novel approach for dimension estimation of topological manifolds based on measures of simplices. We also investigate the effects of resolution changes for dimension estimation in the framework of Morse theory. The result is a method that can be used for data located in simplical complexes of varying dimensions and with no continuous or differentiable structure. The proposed method is applied to images of handwritten digits with known deforming dimensions, data with a nontrivial topology and noisy data. We compare the estimates with results obtain by local PCA.

Place, publisher, year, edition, pages
IEEE COMPUTER SOC , 2016. p. 3609-3614
Series
International Conference on Pattern Recognition, ISSN 1051-4651
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:liu:diva-141751DOI: 10.1109/ICPR.2016.7900194ISI: 000406771303098ISBN: 978-1-5090-4847-2 (print)OAI: oai:DiVA.org:liu-141751DiVA, id: diva2:1147259
Conference
23rd International Conference on Pattern Recognition (ICPR)
Available from: 2017-10-05 Created: 2017-10-05 Last updated: 2018-01-13

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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