Improving the Structuring Capabilities of Statistics–Based Local Learners

  • Slobodan Vukanović
  • Robert Haschke
  • Helge Ritter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8249)


Function approximation, a mainstay of machine learning, is a useful tool in science and engineering. Local learning approches subdivide the learning space into regions to be approximated locally by linear models. An arrangement of regions that conforms to the structure of the target function leads to learning with fewer resources and gives an insight into the function being approximated. This paper introduces a covariance–based update for the size and shape of each local region. An evaluation shows that the method improves the structuring capabilities of state–of–the–art statistics–based local learners.


Function Approximation Locally Weighted Regression Input Space Structuring 


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  1. 1.
    Atkeson, C.G., Moore, A.W., Schaal, S.: Locally weighted learning for control. Artificial Intelligence Review 11, 11–73 (1997)CrossRefGoogle Scholar
  2. 2.
    Finch, T.: Incremental calculation of weighted mean and variance. University of Cambridge (2009)Google Scholar
  3. 3.
    Flentge, F.: Locally weighted interpolating growing neural gas. IEEE Transactions on Neural Networks 17(6), 1382–1393 (2006)CrossRefGoogle Scholar
  4. 4.
    Nguyen-tuong, D., Peters, J.: Local gaussian process regression for real-time model-based robot control. In: Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2008, pp. 380–385 (2008)Google Scholar
  5. 5.
    Ritter, H., Martinetz, T., Schulten, K.: Neural computation and self-organizing maps - an introduction. Computation and neural systems series. Addison-Wesley (1992)Google Scholar
  6. 6.
    Schaal, S., Atkeson, C.G.: Constructive incremental learning from only local information. Neural Computation 10, 2047–2084 (1997)CrossRefGoogle Scholar
  7. 7.
    Sigaud, O., Salaun, C., Padois, V.: On-line regression algorithms for learning mechanical models of robots: a survey. Robotics and Autonomous Systems 59(12), 1115–1129 (2011)CrossRefGoogle Scholar
  8. 8.
    Stalph, P.O., Rubinsztajn, J., Sigaud, O., Butz, M.V.: A comparative study: function approximation with LWPR and XCSF. In: GECCO (Companion), pp. 1863–1870 (2010)Google Scholar
  9. 9.
    Vijayakumar, S., D’Souza, A., Schaal, S.: Incremental online learning in high dimensions. Neural Computation 17, 2602–2634 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wilson, S.W.: Classifiers that approximate functions. Natural Computing 1(2-3), 211–234 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Slobodan Vukanović
    • 1
  • Robert Haschke
    • 1
  • Helge Ritter
    • 1
  1. 1.Cognitive Interaction Technology – Center of Excellence (CITEC)Bielefeld UniversityBielefeldGermany

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