Nonlinear dimensionality reduction using circuit models

Fredrik Andersson, Jens Nilsson

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingResearchpeer-review

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.
Original languageEnglish
Title of host publicationLecture Notes in Computer Science
PublisherSpringer
Pages950-959
Volume3540
DOIs
Publication statusPublished - 2005
Event14th Scandinavian Conference on Image Analysis, SCIA 2005 - Joensuu, Finland
Duration: 2005 Jun 192005 Jun 22

Publication series

Name
Volume3540
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Scandinavian Conference on Image Analysis, SCIA 2005
Country/TerritoryFinland
CityJoensuu
Period2005/06/192005/06/22

Subject classification (UKÄ)

  • Mathematics

Keywords

  • Topological instability
  • Laplacian Eigenmaps
  • Manifold learning
  • Isomap
  • Multidimensional scaling

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