Nonlinear dimensionality reduction using circuit models
(2005) 14th Scandinavian Conference on Image Analysis, SCIA 2005 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/615654
- author
- Andersson, Fredrik LU and Nilsson, Jens LU
- organization
- publishing date
- 2005
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Topological instability, Laplacian Eigenmaps, Manifold learning, Isomap, Multidimensional scaling
- host publication
- Lecture Notes in Computer Science
- volume
- 3540
- pages
- 950 - 959
- publisher
- Springer
- conference name
- 14th Scandinavian Conference on Image Analysis, SCIA 2005
- conference location
- Joensuu, Finland
- conference dates
- 2005-06-19 - 2005-06-22
- 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
- 2016-04-01 12:09:02
- date last changed
- 2024-01-08 10:10:15
@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}},
keywords = {{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}},
doi = {{10.1007/11499145_96}},
volume = {{3540}},
year = {{2005}},
}