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A circuit framework for robust manifold learning

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Author

  • Jens Nilsson
  • Fredrik Andersson

Summary, in English

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.

Publishing year

2007

Language

English

Pages

323-332

Publication/Series

Neurocomputing

Volume

71

Issue

1-3

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

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

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0925-2312