A circuit framework for robust manifold learning

Jens Nilsson, Fredrik Andersson

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)323-332
Issue number1-3
Publication statusPublished - 2007

Subject classification (UKÄ)

  • Mathematics


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


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