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A circuit framework for robust manifold learning

Nilsson, Jens LU and Andersson, Fredrik LU (2007) In Neurocomputing 71(1-3). p.323-332
Abstract
Manifold learning and nonlinear dimensionality reduction addresses the problem of detecting possibly nonlinear structure in highdimensional data and constructing lower-dimensional configurations representative of this structure. A popular example is the Isomap algorithm which uses local information to approximate geodesic distances and adopts multidimensional scaling to produce lowerdimensional representations. Isomap is accurate on a global scale in contrast to many competing methods which approximate locally. However, a drawback of the Isomap algorithm is that it is topologically instable, that is, incorrectly chosen algorithm parameters or perturbations of data may drastically change the resulting configurations. We propose new methods... (More)
Manifold learning and nonlinear dimensionality reduction addresses the problem of detecting possibly nonlinear structure in highdimensional data and constructing lower-dimensional configurations representative of this structure. A popular example is the Isomap algorithm which uses local information to approximate geodesic distances and adopts multidimensional scaling to produce lowerdimensional representations. Isomap is accurate on a global scale in contrast to many competing methods which approximate locally. However, a drawback of the Isomap algorithm is that it is topologically instable, that is, incorrectly chosen algorithm parameters or perturbations of data may drastically change the resulting configurations. We propose new methods for more robust approximation of the geodesic distances using a viewpoint of electric circuits. In this way, we achieve both the stability of local methods and the global approximation property of global methods, while compromising with local accuracy. This is demonstrated by a study of the performance of the proposed and competing methods on different data sets. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Laplacian Eigenmaps, Manifold learning, Topological instability, Multidimensional scaling, Isomap
in
Neurocomputing
volume
71
issue
1-3
pages
323 - 332
publisher
Elsevier
external identifiers
  • wos:000251500600029
  • scopus:35649011363
ISSN
0925-2312
DOI
10.1016/j.neucom.2006.12.021
language
English
LU publication?
yes
id
3dee640a-ffdd-4f4d-ab27-8430bd21b086 (old id 631097)
date added to LUP
2007-12-11 10:10:51
date last changed
2017-01-01 04:21:00
@article{3dee640a-ffdd-4f4d-ab27-8430bd21b086,
  abstract     = {Manifold learning and nonlinear dimensionality reduction addresses the problem of detecting possibly nonlinear structure in highdimensional data and constructing lower-dimensional configurations representative of this structure. A popular example is the Isomap algorithm which uses local information to approximate geodesic distances and adopts multidimensional scaling to produce lowerdimensional representations. Isomap is accurate on a global scale in contrast to many competing methods which approximate locally. However, a drawback of the Isomap algorithm is that it is topologically instable, that is, incorrectly chosen algorithm parameters or perturbations of data may drastically change the resulting configurations. We propose new methods for more robust approximation of the geodesic distances using a viewpoint of electric circuits. In this way, we achieve both the stability of local methods and the global approximation property of global methods, while compromising with local accuracy. This is demonstrated by a study of the performance of the proposed and competing methods on different data sets.},
  author       = {Nilsson, Jens and Andersson, Fredrik},
  issn         = {0925-2312},
  keyword      = {Laplacian Eigenmaps,Manifold learning,Topological instability,Multidimensional scaling,Isomap},
  language     = {eng},
  number       = {1-3},
  pages        = {323--332},
  publisher    = {Elsevier},
  series       = {Neurocomputing},
  title        = {A circuit framework for robust manifold learning},
  url          = {http://dx.doi.org/10.1016/j.neucom.2006.12.021},
  volume       = {71},
  year         = {2007},
}