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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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 Urheber:
Walder, C1, 2, 3, 4, Autor           
Schölkopf, B1, 3, Autor           
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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 Zusammenfassung: 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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 Datum: 2009-06
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
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 Identifikatoren: BibTex Citekey: 5394
 Art des Abschluß: -

Veranstaltung

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Titel: Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008)
Veranstaltungsort: Vancouver, BC, Canada
Start-/Enddatum: 2008-12-08 - 2008-12-10

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Titel: Advances in neural information processing systems 21
Genre der Quelle: Konferenzband
 Urheber:
Koller, D, Herausgeber
Schuurmans, D, Herausgeber
Bengio, Y, Herausgeber
Bottou, L, Herausgeber
Affiliations:
-
Ort, Verlag, Ausgabe: Red Hook, NY, USA : Curran
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 1713 - 1720 Identifikator: ISBN: 978-1-60560-949-2