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A Comparative Study of LOWESS and RBF Approximations for Visualization

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Computational Science and Its Applications – ICCSA 2016 (ICCSA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9787))

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Abstract

Approximation methods are widely used in many fields and many techniques have been published already. This comparative study presents a comparison of LOWESS (Locally weighted scatterplot smoothing) and RBF (Radial Basis Functions) approximation methods on noisy data as they use different approaches. The RBF approach is generally convenient for high dimensional scattered data sets. The LOWESS method needs finding a subset of nearest points if data are scattered. The experiments proved that LOWESS approximation gives slightly better results than RBF in the case of lower dimension, while in the higher dimensional case with scattered data the RBF method has lower computational complexity.

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Abbreviations

D: :

dimension

K: :

k-nearest points

M: :

number of radial basis functions for approximation

N: :

number of all input points

R: :

number of points at which the approximation is calculated

ξ: :

point where to calculate the approximation

d: :

degree of polynomial

r: :

r = d + 2

q: :

q = d + 1

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Acknowledgements

The authors would like to thank their colleagues at the University of West Bohemia, Plzen, for their comments and suggestions, and anonymous reviewers for their valuable critical comments and advice. The research was supported by MSMT CR projects LH12181 and SGS 2016-013.

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Authors and Affiliations

  1. Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, 30614, Pilsen, Czech Republic

    Michal Smolik, Vaclav Skala & Ondrej Nedved

Authors
  1. Michal Smolik
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  2. Vaclav Skala
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  3. Ondrej Nedved
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Corresponding author

Correspondence to Michal Smolik .

Editor information

Editors and Affiliations

  1. University of Perugia , Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata , Potenza, Italy

    Beniamino Murgante

  3. Covenant University , Ota, Nigeria

    Sanjay Misra

  4. University of Minho , Braga, Portugal

    Ana Maria A.C. Rocha

  5. Polytechnic University , Bari, Italy

    Carmelo M. Torre

  6. Monash University , Clayton, Victoria, Australia

    David Taniar

  7. Kyushu Sangyo University , Fukuoka, Japan

    Bernady O. Apduhan

  8. Saint Petersburg State University , Saint Petersburg, Russia

    Elena Stankova

  9. Beijing University of Posts & Telecommunication , Beijing, China

    Shangguang Wang

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Smolik, M., Skala, V., Nedved, O. (2016). A Comparative Study of LOWESS and RBF Approximations for Visualization. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9787. Springer, Cham. https://doi.org/10.1007/978-3-319-42108-7_31

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  • DOI: https://doi.org/10.1007/978-3-319-42108-7_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42107-0

  • Online ISBN: 978-3-319-42108-7

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