Geometrical Complexity of Data Approximators

  • Evgeny M. Mirkes
  • Andrei Zinovyev
  • Alexander N. Gorban
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7902)


There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.


Data analysis Approximation algorithms Data structures Data complexity Model selection 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Evgeny M. Mirkes
    • 1
  • Andrei Zinovyev
    • 2
    • 3
    • 4
  • Alexander N. Gorban
    • 1
  1. 1.Department of MathematicsUniversity of LeicesterUK
  2. 2.Institut CurieParisFrance
  3. 3.INSERM U900ParisFrance
  4. 4.Mines ParisTechFontainebleauFrance

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