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Fast manifold learning based on Riemannian normal coordinates
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
Laboratory of Mathematics in Imaging Harvard Medical School, Boston, USA.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).ORCID iD: 0000-0002-9091-4724
2005 (English)In: Image Analysis: 14th Scandinavian Conference, SCIA 2005, Joensuu, Finland, June 19-22, 2005. Proceedings, Springer Berlin/Heidelberg, 2005, 920- p.Conference paper, Published paper (Refereed)
Abstract [en]

We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of data points in order to perform dimension reduction. Our implementation currently uses Dijkstra’s algorithm for shortest paths in graphs and some basic concepts from differential geometry. We expect this approach to open up new possibilities for analysis of e.g. shape in medical imaging and signal processing of manifold-valued signals, where the coordinate system is “learned” from experimental high-dimensional data rather than defined analytically using e.g. models based on Lie-groups.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2005. 920- p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 3540
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-28773DOI: 10.1007/11499145_93Local ID: 13955ISBN: 978-3-540-26320-3 (print)ISBN: 978-3-540-31566-7 (print)OAI: oai:DiVA.org:liu-28773DiVA: diva2:249585
Conference
14th Scandinavian Conference, SCIA 2005, Joensuu, Finland, June 19-22, 2005
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-08-28Bibliographically approved

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Brun, AndersWestin, Carl-FredrikHerberthson, MagnusKnutsson, Hans

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Citation style
  • apa
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