A circuit framework for robust manifold learning

Research output: Contribution to journalArticle


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.


  • Jens Nilsson
  • Fredrik Andersson
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Laplacian Eigenmaps, Manifold learning, Topological instability, Multidimensional scaling, Isomap
Original languageEnglish
Pages (from-to)323-332
Issue number1-3
Publication statusPublished - 2007
Publication categoryResearch

Related research output

Jens Nilsson, 2006, 108 p.

Research output: ThesisLicentiate Thesis

Fredrik Andersson & Jens Nilsson, 2005, Lecture Notes in Computer Science. Springer, Vol. 3540. p. 950-959

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

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