Diffeomorphic Dimensionality Reduction

Walder, C; Schölkopf, B

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Diffeomorphic Dimensionality Reduction

Walder, C., & Schölkopf, B. (2009). Diffeomorphic Dimensionality Reduction. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems 21 (pp. 1713-1720). Red Hook, NY, USA: Curran.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-C479-8 Version Permalink: https://hdl.handle.net/21.11116/0000-0003-1DA2-6

Genre: Conference Paper

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https://papers.nips.cc/paper/3542-diffeomorphic-dimensionality-reduction.pdf (Publisher version) Open Access status unknown

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Creators:
Walder, C^{1, 2, 3, 4}, Author
Schölkopf, B^{1, 3}, Author

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
3Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794
4Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_2528702

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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: Date issued: 2009-06

Publication Status: Issued

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Identifiers: BibTex Citekey: 5394

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Title: Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008)

Place of Event: Vancouver, BC, Canada

Start-/End Date: 2008-12-08 - 2008-12-10

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Title: Advances in neural information processing systems 21

Source Genre: Proceedings

Creator(s):
Koller, D, Editor
Schuurmans, D, Editor
Bengio, Y, Editor
Bottou, L, Editor

Affiliations:
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Publ. Info: Red Hook, NY, USA : Curran

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1713 - 1720 Identifier: ISBN: 978-1-60560-949-2