Skip to main content
SpringerLink
Log in
Book cover

International Conference on P2P, Parallel, Grid, Cloud and Internet Computing

3PGCIC 2017: Advances on P2P, Parallel, Grid, Cloud and Internet Computing pp 807–818Cite as

Non Linear Fitting Methods for Machine Learning

  • Conference paper
  • First Online:

  • 1397 Accesses

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 13))

Abstract

This manuscript presents an analysis of numerical fitting methods used for solving classification problems as discriminant functions in machine learning. Non linear polynomial, exponential, and trigonometric models are mathematically deduced and discussed. Analysis about their pros and cons, and their mathematical modelling are made on what method to chose for what type of highly non linear multi-dimension problems are more suitable to be solved. In this study only deterministic models with analytic solutions are involved, or parameters calculation by numeric methods, which the complete model can subsequently be treated as a theoretical model. Models deduction are summarised and presented as a survey.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

References

  1. Jabbar, H.K., Khan, R.Z.: Methods to avoid over-fitting and under-fitting in supervised machine learning (comparative study). Comp. Sci., Comm. Instr. Dev. 163–172 (2015)

    Google Scholar 

  2. Tetko, I.V., Livingstone, D.J., Luik, A.I.: Neural network studies. 1. Comparison of overfitting and overtraining. J. Chem. Inf. Comput. Sci. 35, 826–833 (1995)

    Article  Google Scholar 

  3. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)

    MATH  Google Scholar 

  4. Riley, K.F., Hobson, M.P., Bence, S.J.: Mathematical Methods for Physics and Engineering, 3rd edn. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  5. Cheney, W., Kincais, D.: Numerical Mathematics and Computing, 6th edn. Cengage, Boston (2011)

    Google Scholar 

  6. Kreyszig, E.: Advanced Engineering Mathematics, 3rd edn. Limusa Wiley, Mexico City (2009)

    MATH  Google Scholar 

  7. Van, D.A., Rubin, W.M., Rubin, V., Verbeek, H.M.W., Van Dongen, B.F., Kindler, E., Gunther, C.W.: Process mining: a two-step approach to balance between underfitting and overfitting. Softw. Syst. Model. 9(1), 87–111 (2010)

    Article  Google Scholar 

  8. Loughrey, J., Cunningham, P.: Using early-stopping to avoid overfitting in wrapper- based feature selection employing stochastic search (2005)

    Google Scholar 

  9. Schaffer, C.: Overfitting avoidance as bias. Mach. Learn. 10(2), 153–178 (1993)

    Google Scholar 

  10. Ruppert, D., Carroll, R.J.: Spatially-adaptive penalties for spline fitting. J. Statist. 42, 205–224 (2000)

    Google Scholar 

  11. Lawrence, S., Giles, C.L., Tsoi, A.C.: Lessons in neural network training: overfitting may be harder than expected. In: Proceedings of the 14th National Conference on AI, USA, pp. 540–545 (1997)

    Google Scholar 

  12. Raskutti, G., Wainwright, M.J., Yu, B.: Early stopping and non-parametric regression: an optimal data-dependent stopping rule. J. Mach. Learn. Res. 15(1), 335–366 (2014)

    MATH  MathSciNet  Google Scholar 

  13. Bishop, C.M.: Neural Networks for Patter Recognition. Oxford University Press, Oxford (2005)

    Google Scholar 

  14. Freeman, J.A., Skapura, D.M.: Neural Networks, Algorithms, Applications and Programming Techniques. Computation and Neural Systems Series. Addison-Wesley, Reading (2002)

    MATH  Google Scholar 

  15. Wen, U.P., Lan, K.M., Shih, H.S.: A review of Hopfield neural networks for solving mathematical programming problems. Eur. J. Oper. Res. 198(3), 675–687 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Caruana, R., Lawrence, S., Giles, L.: Overfitting in neural nets: backpropagation, conjugate gradient, and early stopping. In: Advances in Neural Information Processing Systems, pp. 402–408 (2011)

    Google Scholar 

  17. Kazushi, M.: Avoiding overfitting in multilayer perceptrons with feeling-of-knowing using self-organizing maps. Biosystems 80(1), 37–40 (2005)

    Article  Google Scholar 

  18. Gaurang, P., Amit, G., Parth, S., Devyani, P.: Determination Of over-learning and over-fitting problem in back propagation neural network. Int. J. Soft Comput. 2(2), 40–51 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Mexico

    Edgar A. Martínez-García & Ricardo Rodríguez-Jorge

  2. University of Texas at El Paso, El Paso, USA

    Nancy Ávila Rodríguez

  3. Opole University, Opole, Poland

    Jolanta Mizera-Pietraszko

  4. Singapore Polytechnic, Singapore, Singapore

    Jaichandar Kulandaidaasan Sheba

  5. Singapore University of Technology and Design, Singapore, Singapore

    Rajesh Elara Mohan

  6. Kazan Federal University, Kazan, Russian Federation

    Evgeni Magid

Authors
  1. Edgar A. Martínez-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nancy Ávila Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ricardo Rodríguez-Jorge
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jolanta Mizera-Pietraszko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jaichandar Kulandaidaasan Sheba
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Rajesh Elara Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Evgeni Magid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edgar A. Martínez-García .

Editor information

Editors and Affiliations

  1. Technical University of Catalonia, Barcelona, Spain

    Fatos Xhafa

  2. Open University of Catalonia, Barcelona, Spain

    Santi Caballé

  3. Fukuoka Institute of Technology (FIT), Fukuoka, Japan

    Leonard Barolli

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Martínez-García, E.A. et al. (2018). Non Linear Fitting Methods for Machine Learning. In: Xhafa, F., Caballé, S., Barolli, L. (eds) Advances on P2P, Parallel, Grid, Cloud and Internet Computing. 3PGCIC 2017. Lecture Notes on Data Engineering and Communications Technologies, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-69835-9_76

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-69835-9_76

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69834-2

  • Online ISBN: 978-3-319-69835-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation