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Computing

, Volume 75, Issue 4, pp 359–379 | Cite as

Elastic Principal Graphs and Manifolds and their Practical Applications

  • A. GorbanEmail author
  • A. Zinovyev
Article

Abstract

Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through “the middle” of data distribution. We propose an algorithm for fast construction of grid approximations of principal manifolds with given topology. It is based on analogy of principal manifold and elastic membrane. First advantage of this method is a form of the functional to be minimized which becomes quadratic at the step of the vertices position refinement. This makes the algorithm very effective, especially for parallel implementations. Another advantage is that the same algorithmic kernel is applied to construct principal manifolds of different dimensions and topologies. We demonstrate how flexibility of the approach allows numerous adaptive strategies like principal graph constructing, etc. The algorithm is implemented as a C++ package elmap and as a part of stand-alone data visualization tool VidaExpert, available on the web. We describe the approach and provide several examples of its application with speed performance characteristics.

AMS Subject Classifications

62H25 62-07 62-09 68P05 

Keywords

Principal manifolds elastic functional data analysis data visualization surface modeling 

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Copyright information

© Springer-Verlag Wien 2005

Authors and Affiliations

  1. 1.University of LeicesterLeicesterUK
  2. 2.Institut CurieParisFrance

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