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Diffeomorphic Dimensionality Reduction

2009

Conference Paper

ei


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.

Author(s): Walder, C. and Schölkopf, B.
Book Title: Advances in neural information processing systems 21
Journal: Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008
Pages: 1713-1720
Year: 2009
Month: June
Day: 0
Editors: D Koller and D Schuurmans and Y Bengio and L Bottou
Publisher: Curran

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 22nd Annual Conference on Neural Information Processing Systems (NIPS 2008)
Event Place: Vancouver, BC, Canada

Address: Red Hook, NY, USA
Digital: 0
ISBN: 978-1-605-60949-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{5394,
  title = {Diffeomorphic Dimensionality Reduction},
  author = {Walder, C. and Sch{\"o}lkopf, B.},
  journal = {Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008},
  booktitle = {Advances in neural information processing systems 21},
  pages = {1713-1720},
  editors = {D Koller and D Schuurmans and Y Bengio and L Bottou},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}