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Nonlinear dimensionality reduction using circuit models

Andersson, Fredrik LU and Nilsson, Jens LU (2005) 14th Scandinavian Conference on Image Analysis, SCIA 2005 In Lecture Notes in Computer Science 3540. p.950-959
Abstract
The problem addressed in nonlinear dimensionality reduction, is to find lower dimensional configurations of high dimensional data, thereby revealing underlying structure. One popular method in this regard is the Isomap algorithm, where local information is used to find approximate geodesic distances. From such distance estimations, lower dimensional representations, accurate on a global scale, are obtained by multidimensional scaling. The property of global approximation sets Isomap in contrast to many competing methods, which approximate only locally. A serious drawback of Isomap is that it is topologically instable, i.e., that incorrectly chosen algorithm parameters or perturbations of data may abruptly alter the resulting... (More)
The problem addressed in nonlinear dimensionality reduction, is to find lower dimensional configurations of high dimensional data, thereby revealing underlying structure. One popular method in this regard is the Isomap algorithm, where local information is used to find approximate geodesic distances. From such distance estimations, lower dimensional representations, accurate on a global scale, are obtained by multidimensional scaling. The property of global approximation sets Isomap in contrast to many competing methods, which approximate only locally. A serious drawback of Isomap is that it is topologically instable, i.e., that incorrectly chosen algorithm parameters or perturbations of data may abruptly alter the resulting configurations. To handle this problem, we propose new methods for more robust approximation of the geodesic distances. This is done using a viewpoint of electric circuits. The robustness is validated by experiments. By such an approach we achieve both the stability of local methods and the global approximation property of global methods. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Topological instability, Laplacian Eigenmaps, Manifold learning, Isomap, Multidimensional scaling
in
Lecture Notes in Computer Science
volume
3540
pages
950 - 959
publisher
Springer
conference name
14th Scandinavian Conference on Image Analysis, SCIA 2005
external identifiers
  • scopus:26444590964
  • wos:000230372500096
ISSN
1611-3349
0302-9743
DOI
10.1007/11499145_96
language
English
LU publication?
yes
id
cb740ce8-78d1-45ff-b031-1738aed4b8cc (old id 615654)
date added to LUP
2007-11-25 09:08:06
date last changed
2017-01-01 04:53:10
@inproceedings{cb740ce8-78d1-45ff-b031-1738aed4b8cc,
  abstract     = {The problem addressed in nonlinear dimensionality reduction, is to find lower dimensional configurations of high dimensional data, thereby revealing underlying structure. One popular method in this regard is the Isomap algorithm, where local information is used to find approximate geodesic distances. From such distance estimations, lower dimensional representations, accurate on a global scale, are obtained by multidimensional scaling. The property of global approximation sets Isomap in contrast to many competing methods, which approximate only locally. A serious drawback of Isomap is that it is topologically instable, i.e., that incorrectly chosen algorithm parameters or perturbations of data may abruptly alter the resulting configurations. To handle this problem, we propose new methods for more robust approximation of the geodesic distances. This is done using a viewpoint of electric circuits. The robustness is validated by experiments. By such an approach we achieve both the stability of local methods and the global approximation property of global methods.},
  author       = {Andersson, Fredrik and Nilsson, Jens},
  booktitle    = {Lecture Notes in Computer Science},
  issn         = {1611-3349},
  keyword      = {Topological instability,Laplacian Eigenmaps,Manifold learning,Isomap,Multidimensional scaling},
  language     = {eng},
  pages        = {950--959},
  publisher    = {Springer},
  title        = {Nonlinear dimensionality reduction using circuit models},
  url          = {http://dx.doi.org/10.1007/11499145_96},
  volume       = {3540},
  year         = {2005},
}