Fast manifold learning based on Riemannian normal coordinates
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 (Refereed)
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.
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online) ; 3540
Medical and Health Sciences
IdentifiersURN: urn:nbn:se:liu:diva-28773DOI: 10.1007/11499145_93Local ID: 13955ISBN: 978-3-540-26320-3 (print)ISBN: 978-3-540-31566-7 (online)OAI: oai:DiVA.org:liu-28773DiVA: diva2:249585
14th Scandinavian Conference, SCIA 2005, Joensuu, Finland, June 19-22, 2005