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A New Strategy for Scattered Data Approximation Using Radial Basis Functions Respecting Points of Inflection

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11619))

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Abstract

The approximation of scattered data is known technique in computer science. We propose a new strategy for the placement of radial basis functions respecting points of inflection. The placement of radial basis functions has a great impact on the approximation quality. Due to this fact we propose a new strategy for the placement of radial basis functions with respect to the properties of approximated function, including the extreme and the inflection points. Our experimental results proved high quality of the proposed approach and high quality of the final approximation.

The research was supported by projects Czech Science Foundation (GACR) No. 17-05534S and partially by SGS 2019-016.

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References

  1. Afiatdoust, F., Esmaeilbeigi, M.: Optimal variable shape parameters using genetic algorithm for radial basis function approximation. Ain Shams Engineering J. 6(2), 639–647 (2015)

    Article  Google Scholar 

  2. Biazar, J., Hosami, M.: Selection of an interval for variable shape parameter in approximation by radial basis functions. In: Advances in Numerical Analysis 2016 (2016)

    Google Scholar 

  3. Chen, S., Chng, E., Alkadhimi, K.: Regularized orthogonal least squares algorithm for constructing radial basis function networks. Int. J. Control 64(5), 829–837 (1996)

    Article  MathSciNet  Google Scholar 

  4. Fasshauer, G.E.: Meshfree Approximation Methods with MATLAB, vol. 6. World Scientific (2007)

    Google Scholar 

  5. Fornberg, B., Wright, G.: Stable computation of multiquadric interpolants for all values of the shape parameter. Comput. Math. Appl. 48(5–6), 853–867 (2004)

    Article  MathSciNet  Google Scholar 

  6. Franke, R.: A critical comparison of some methods for interpolation of scattered data. Technical report, Naval Postgraduate School Monterey CA (1979)

    Google Scholar 

  7. Ghosh-Dastidar, S., Adeli, H., Dadmehr, N.: Principal component analysis-enhanced cosine radial basis function neural network for robust epilepsy and seizure detection. IEEE Trans. Biomed. Eng. 55(2), 512–518 (2008)

    Article  Google Scholar 

  8. Hardy, R.L.: Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 76(8), 1905–1915 (1971)

    Article  Google Scholar 

  9. Hardy, R.L.: Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988. Comput. Mathe. Appl. 19(8–9), 163–208 (1990)

    Article  MathSciNet  Google Scholar 

  10. Karim, A., Adeli, H.: Radial basis function neural network for work zone capacity and queue estimation. J. Transp. Eng. 129(5), 494–503 (2003)

    Article  Google Scholar 

  11. Larsson, E., Fornberg, B.: A numerical study of some radial basis function based solution methods for elliptic PDEs. Comput. Math. Appl. 46(5), 891–902 (2003)

    Article  MathSciNet  Google Scholar 

  12. Majdisova, Z., Skala, V.: Big geo data surface approximation using radial basis functions: a comparative study. Comput. Geosci. 109, 51–58 (2017)

    Article  Google Scholar 

  13. Majdisova, Z., Skala, V.: Radial basis function approximations: comparison and applications. Appl. Math. Model. 51, 728–743 (2017)

    Article  MathSciNet  Google Scholar 

  14. Majdisova, Z., Skala, V., Smolik, M.: Determination of stationary points and their bindings in dataset using RBF methods. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds.) CoMeSySo 2018. AISC, vol. 859, pp. 213–224. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-00211-4_20

    Chapter  Google Scholar 

  15. Orr, M.J.: Regularised centre recruitment in radial basis function networks. Centre for Cognitive Science, Edinburgh University. Citeseer (1993)

    Google Scholar 

  16. Orr, M.J.: Regularization in the selection of radial basis function centers. Neural Comput. 7(3), 606–623 (1995)

    Article  Google Scholar 

  17. Pan, R., Skala, V.: A two-level approach to implicit surface modeling with compactly supported radial basis functions. Eng. Comput. 27(3), 299–307 (2011)

    Article  Google Scholar 

  18. Pan, R., Skala, V.: Surface reconstruction with higher-order smoothness. Vis. Comput. 28(2), 155–162 (2012)

    Article  Google Scholar 

  19. Prakash, G., Kulkarni, M., Sripati, U.: Using RBF neural networks and Kullback-Leibler distance to classify channel models in free space optics. In: 2012 International Conference on Optical Engineering (ICOE), pp. 1–6. IEEE (2012)

    Google Scholar 

  20. Sarra, S.A., Sturgill, D.: A random variable shape parameter strategy for radial basis function approximation methods. Eng. Anal. Bound. Elem. 33(11), 1239–1245 (2009)

    Article  MathSciNet  Google Scholar 

  21. Schagen, I.P.: Interpolation in two dimensions - a new technique. IMA J. Appl. Math. 23(1), 53–59 (1979)

    Article  MathSciNet  Google Scholar 

  22. Skala, V.: Fast interpolation and approximation of scattered multidimensional and dynamic data using radial basis functions. WSEAS Trans. Math. 12(5), 501–511 (2013)

    Google Scholar 

  23. Skala, V.: RBF interpolation with CSRBF of large data sets. Procedia Comput. Sci. 108, 2433–2437 (2017)

    Article  Google Scholar 

  24. Smolik, M., Skala, V.: Spherical RBF vector field interpolation: experimental study. In: 2017 IEEE 15th International Symposium on Applied Machine Intelligence and Informatics (SAMI), pp. 000431–000434. IEEE (2017)

    Google Scholar 

  25. Smolik, M., Skala, V.: Large scattered data interpolation with radial basis functions and space subdivision. Integr. Comput.-Aided Eng. 25(1), 49–62 (2018)

    Article  Google Scholar 

  26. Smolik, M., Skala, V., Majdisova, Z.: Vector field radial basis function approximation. Adv. Eng. Softw. 123(1), 117–129 (2018)

    Article  Google Scholar 

  27. Smolik, M., Skala, V., Nedved, O.: A comparative study of LOWESS and RBF approximations for visualization. In: Gervasi, O., et al. (eds.) ICCSA 2016. LNCS, vol. 9787, pp. 405–419. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42108-7_31

    Chapter  Google Scholar 

  28. Uhlir, K., Skala, V.: Reconstruction of damaged images using radial basis functions. In: 2005 13th European Signal Processing Conference, pp. 1–4. IEEE (2005)

    Google Scholar 

  29. Wang, J., Liu, G.: On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Methods Appl. Mech. Eng. 191(23–24), 2611–2630 (2002)

    Article  MathSciNet  Google Scholar 

  30. Wendland, H.: Computational aspects of radial basis function approximation. Stud. Comput. Math. 12, 231–256 (2006)

    Article  MathSciNet  Google Scholar 

  31. Wright, G.B.: Radial basis function interpolation: numerical and analytical developments (2003)

    Google Scholar 

  32. Yingwei, L., Sundararajan, N., Saratchandran, P.: Performance evaluation of a sequential minimal radial basis function (RBF) neural network learning algorithm. IEEE Trans. Neural Netw. 9(2), 308–318 (1998)

    Article  Google Scholar 

  33. Zhang, X., Song, K.Z., Lu, M.W., Liu, X.: Meshless methods based on collocation with radial basis functions. Comput. Mech. 26(4), 333–343 (2000)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank their colleagues at the University of West Bohemia, Plzen, for their discussions and suggestions, and anonymous reviewers for their valuable comments and hints provided. The research was supported by projects Czech Science Foundation (GACR) No. 17-05534S and partially by SGS 2019-016.

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Authors and Affiliations

  1. Faculty of Applied Sciences, University of West Bohemia, Plzen, Czech Republic

    Martin Cervenka, Michal Smolik & Vaclav Skala

Authors
  1. Martin Cervenka
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  2. Michal Smolik
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  3. Vaclav Skala
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Corresponding author

Correspondence to Michal Smolik .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Cervenka, M., Smolik, M., Skala, V. (2019). A New Strategy for Scattered Data Approximation Using Radial Basis Functions Respecting Points of Inflection. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11619. Springer, Cham. https://doi.org/10.1007/978-3-030-24289-3_24

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  • DOI: https://doi.org/10.1007/978-3-030-24289-3_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24288-6

  • Online ISBN: 978-3-030-24289-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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