Skip to main content
SpringerLink
Log in

Symbolic Regression

  • Chapter
  • First Online:
Geospatial Algebraic Computations

Abstract

Symbolic regression (SR) is the process of determining the symbolic function, which describes a data set-effectively developing an analytic model, which summarizes the data and is useful for predicting response behaviors as well as facilitating human insight and understanding. The symbolic regression approach adopted herein is based upon genetic programming wherein a population of functions are allowed to breed and mutate with the genetic propagation into subsequent generations based upon a survival-of-the-fittest criteria. Amazingly, this works and, although computationally intensive, summary solutions may be reasonably discovered using current laptop and desktop computers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Babu BV, Karthik S (2007) Genetic programming for symbolic regression of chemical process systems. Eng Lett 14:2. EL-14 2 6 (advanced on line publication)

    Google Scholar 

  2. Banks C (2002) Searching for Lyapunov functions using genetic programming. Technical report, Virginia Polytechnic Institute and State University, Blacksburg

    Google Scholar 

  3. Cramer NL (1985) A representation for the adaptive generation of simple sequential programs. In: Grefenstette JJ (ed) Proceedings of the 1st International Conference on Genetic Algorithms and Their Applications, Erlbaum, pp 183–187

    Google Scholar 

  4. Davidson JW, Savic DA, Walters GA (2003) Symbolic and numerical regression: experiments and applications. Inf Sci 150(12):95–117

    Article  Google Scholar 

  5. Featherstone W (2000) Refinement of gravimetric geoid using GPS and levelling data. J Surv Eng 126(2):27–56

    Article  Google Scholar 

  6. Ferreira C (2006) Gene expression programming: mathematical modeling by an artificial intelligence, 2nd edn. Springer, Berlin

    Google Scholar 

  7. Fotopoulos G (2005) Calibration of geoid errormodels via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data. J Geod 79(1–3):111–123

    Article  Google Scholar 

  8. Fotopoulos G, Sideris MG (2005) Spatial modeling and analysis of adjusted residuals over a network of GPS-levelling bench marks. Geomatica 59(3):251–262

    Google Scholar 

  9. Fasshauer GE (2007) Meshfree approximation methods with MATLAB. World Scientific Publishing, New Jersey/London

    Book  Google Scholar 

  10. Garg A, Tai K (2011) A hybrid genetic programmingartificial neural network approach for modeling of vibratory finishing process. In: 2011 International Conference on Information and Intelligent Computing IPCSIT, vol 18. IACSIT, Singapore, pp 14–19

    Google Scholar 

  11. Iliffe JC, Ziebart M, Cross PA, Forsberg R, Strykowski G, Tscherning CC (2003) OGSM02: a new model for converting GPS-derived heights to local height datums in Great Britain and Ireland. Surv Rev 37(290):276–293

    Article  Google Scholar 

  12. Kavzoglu T, Saka MH (2005) Modelling local GPS/levelling geoid undulations using artificial neural networks. J Geod 78:520–527

    Google Scholar 

  13. Kecman V (2001) Learning and soft computing: support vector machines, neural networks, and fuzzy logic models (complex adaptive systems). MIT, Cambridge

    Google Scholar 

  14. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. The MIT Press, Cambridge

    Google Scholar 

  15. Kwon YK, Moon BR (2005) Critical heat flux function approximation using genetic algorithms. IEEE Trans Nucl Sci 52(2):535–545

    Article  Google Scholar 

  16. Langdon WB, Gustafson SM (2010) Geneteic programming and evolvable machines: 10 years of reviews. Genet Program Evolvable Mach 11:321–338

    Article  Google Scholar 

  17. Lin KC, Wang J (1995) Transformation from geocentric to geodetic coordinates using Newton’s iteration. Bull Geod 69:300–303

    Article  Google Scholar 

  18. Morales CO (2004) Symbolic regression problems by genetic programming with multi-branches. In: MICAI 2004: Advances in Artificial Intelligence, Mexico City, pp 717–726

    Google Scholar 

  19. Nahavandchi H, Soltanpour A (2004) An attempt to define a new height datum in Norvay. The Geodesy and Hydrography days, 4–5 Nov. Sandnes, Norway

    Google Scholar 

  20. Paláncz B, Völgyesi L, Popper Gy (2005) Support vector regression via mathematica. Period Polytech Civ Eng 49/1:57–84

    Google Scholar 

  21. Paláncz B, Awange JL (2012) Application of Perato optimality to linear models with errors-in-all-variables. J Geod 86:531–545

    Article  Google Scholar 

  22. Parasuraman K, Elshorbagy A, Carey SK (2007) Modelling the dynamics of the evapotranspiration process using genetic programming. Hydrol Sci J 52(3):563–578. doi:10.1623/hysj.52.3.563

    Article  Google Scholar 

  23. Santini M, Tettamanzi A (2001) Genetic programming for financial time series prediction. In: Genetic Programming. Euro GPO’01 Proceedings, Lake Como. Lectures notes in computer science, vol 2038, pp 361–371

    Google Scholar 

  24. Schmidt M, Lipson H (2009) Distilling free-form natural laws from experimental data. Science 324:81–85

    Article  Google Scholar 

  25. Smits G, Kotanchek M (2004) Pareto-front exploitation in symbolic regression. In: Genetic Programming Theory and Practice II. Springer, Ann Arbor, pp 283–299

    Google Scholar 

  26. Soltanpour A, Nahavandchi H, Featherstone WE (2006) Geoid-type surface determination using waveletbased combination of gravimetric quasi/geoid and GPS/levelling data. Geophys Res Abstr 8:4612

    Google Scholar 

  27. Wu CH, Chou HJ, Su WH (2007) A genetic approach for coordinate transformation test of GPS positioning. IEEE Geosci Remote Sens Lett 4(2):297–301

    Article  Google Scholar 

  28. Wu CH, Chou HJ, Su WH (2008) Direct transformation of coordinates for GPS positioning using techniques of genetic programming and symbolic regression on partitioned data. Eng Appl Artif Intell 21:1347–1359

    Article  Google Scholar 

  29. Wu CH, Su WH (2013) Lattice-based clustering and genetic programming for coordinate transformation in GPS applications. Comput Geosci 52:85–94

    Article  Google Scholar 

  30. Zaletnyik P, Paláncz B, Völgyesi L, Kenyeres A (2007) Correction of the gravimetric geoid using GPS leveling data. Geomatikai Közlemények X:231–240 (In Hungarian)

    Google Scholar 

  31. Zaletnyik P, Völgyesi L, Paláncz B (2008) Modelling local GPS/leveling geoid undulations using support vector machines. Period Polytech Civ Eng 52(1):39–43

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Curtin University, Perth, West Australia, Australia

    Joseph L. Awange

  2. Budapest University of Technology and Economics, Budapest, Hungary

    Béla Paláncz

Authors
  1. Joseph L. Awange
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Béla Paláncz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Awange, J.L., Paláncz, B. (2016). Symbolic Regression. In: Geospatial Algebraic Computations. Springer, Cham. https://doi.org/10.1007/978-3-319-25465-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation