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  Diffeomorphic Dimensionality Reduction

Walder, C., & Schölkopf, B. (2009). Diffeomorphic Dimensionality Reduction. Advances in neural information processing systems 21: 22nd Annual Conference on Neural Information Processing Systems 2008, 1713-1720.

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 Creators:
Walder, C1, 2, Author           
Schölkopf, B1, Author           
Koller, Editor
D., Editor
Schuurmans, D., Editor
Bengio, Y., Editor
Bottou, L., Editor
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              

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 Abstract: This paper introduces a new approach to constructing meaningful lower dimensional representations of sets of data points. We argue that constraining the mapping between the high and low dimensional spaces to be a diffeomorphism is a natural way of ensuring that pairwise distances are approximately preserved. Accordingly we develop an algorithm which diffeomorphically maps the data near to a lower dimensional subspace and then projects onto that subspace. The problem of solving for the mapping is transformed into one of solving for an Eulerian flow field which we compute using ideas from kernel methods. We demonstrate the efficacy of our approach on various real world data sets.

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 Dates: 2009-06
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: ISBN: 978-1-605-60949-2
URI: http://nips.cc/Conferences/2008/
BibTex Citekey: 5394
 Degree: -

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Title: Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008)
Place of Event: Vancouver, BC, Canada
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Title: Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008
Source Genre: Journal
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Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1713 - 1720 Identifier: -