Skip to main content

A New Proposition of the Activation Function for Significant Improvement of Neural Networks Performance

  • Conference paper
  • First Online:
Book cover Artificial Intelligence and Soft Computing (ICAISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9692))

Included in the following conference series:

Abstract

An activation function is a very important part of an artificial neuron model. Multilayer neural networks can properly work only when these functions are nonlinear. A simple approximation of an often applied hyperbolic tangent activation function is presented. This proposed function is computationally highly effective. Computational comparisons for two well-known test problems are discussed. The results are very promising in potential applications to FPGA chips designing.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

References

  1. Bilski, J.: The backpropagation learning with logarithmic transfer function. In: Proceedings of 5th Conference On Neural Networks and Soft Computing, Poland, pp. 71–76 (2000)

    Google Scholar 

  2. Bilski, J., Rutkowski, L.: A fast training algorithm for neural networks. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 45(6), 749–753 (1998)

    Article  Google Scholar 

  3. Bilski, J.: The UD RLS algorithm for training the feedforward neural networks. Int. J. Appl. Math. Comput. Sci. 15(1), 101–109 (2005)

    MATH  Google Scholar 

  4. Bilski, J., Litwiński, S., Smola̧g, J.: Parallel realisation of QR algorithm for neural networks learning. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 158–165. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Bilski, J., Smola̧g, J.: Parallel realisation of the recurrent RTRN neural network learning. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 11–16. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Bilski, J., Smola̧g, J.: Parallel realisation of the recurrent Elman neural network learning. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS(LNAI), vol. 6114, pp. 19–25. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Bilski, J., Smola̧g, J.: Parallel realisation of the recurrent multi layer perceptron learning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS(LNAI), vol. 7267, pp. 12–20. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Bilski, J., Smola̧g, J.: Parallel approach to learning of the recurrent Jordan neural network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS(LNAI), vol. 7894, pp. 32–40. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. Bilski, J.: Parallel Structures for Feedforward and Dynamical Neural Networks. AOW EXIT (2013). (in Polish)

    Google Scholar 

  10. Bilski, J., Smola̧g, J., Galushkin, A.I.: The parallel approach to the conjugate gradient learning algorithm for the feedforward neural networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS(LNAI), vol. 8467, pp. 12–21. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  11. Bilski, J., Smola̧g, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561–2570 (2015)

    Article  Google Scholar 

  12. Bilski, J., Smola̧g, J., Żurada, J.M.: Parallel approach to the Levenberg-Marquardt learning algorithm for feedforward neural networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) Artificial Intelligence and Soft Computing. LNCS(LNAI), vol. 9119, pp. 3–14. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  13. Chu, L.J., Krzyżak, A.: The recognition of partially occluded objects with support vector machines, convolutional neural networks and deep belief networks. J. Artif. Intell. Soft Comput. Res. 4(1), 5–19 (2014)

    Article  Google Scholar 

  14. Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomputing 135, 203–217 (2014)

    Article  Google Scholar 

  15. Cpałka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. Gen. Syst. 42(6), 706–720 (2013)

    Article  MATH  Google Scholar 

  16. Cpałka, K., Zalasiński, M., Rutkowski, L.: New method for the on-line signature verification based on horizontal partitioning. Pattern Recognit. 47, 2652–2661 (2014)

    Article  Google Scholar 

  17. Duch, W., Jankowski, N.: A survey of neural transfer functions. Neural Comput. Surv. 2, 163–213 (1999)

    Google Scholar 

  18. Fahlman, S.: Faster learning variations on back-propagation: an empirical study. In: Proceedings of Connectionist Models Summer School, Los Atos (1988)

    Google Scholar 

  19. Hagan, M.T., Menhaj, M.B.: Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw. 5(6), 989–993 (1994)

    Article  Google Scholar 

  20. Jankowski, N., Duch, W.: Optimal transfer function neural networks. In: Procedings of the 9th European Symposium on Artificial Neural Networks, Bruges, Belgium, pp. 101–106 (2001)

    Google Scholar 

  21. Kamruzzaman, J., Aziz, S.M.: A note on activation function in multilayer feedforward learning. In: Proceedings of International Joint Conference on Neural Networks: IJCNN 2002, vol. 1, pp. 519–523 (2002)

    Google Scholar 

  22. Kitajima, R., Kamimura, R.: Accumulative information enhancement in the self-organizing maps and its application to the analysis of mission statements. J. Artif. Intell. Soft Comput. Res. 5(3), 161–176 (2015)

    Article  Google Scholar 

  23. Korytkowski, M., Rutkowski, L., Scherer, R.: Fast image classification by boosting fuzzy classifiers. Inf. Sci. 327, 175–182 (2016)

    Article  MathSciNet  Google Scholar 

  24. Łapa, K., Zalasiński, M., Cpałka, K.: A new method for designing and complexity reduction of neuro-fuzzy systems for nonlinear modelling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS(LNAI), vol. 7894, pp. 329–344. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  25. Riedmiller, M., Braun, H.: A direct method for faster backpropagation learning: the RPROP algorithm. In: IEEE International Conference on Neural Networks, San Francisco (1993)

    Google Scholar 

  26. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Rumelhart, D.E., McClelland, J.L. (eds.) Parallel Distributed Processing, vol. 1, chap. 8. The MIT Press, Cambridge (1986)

    Google Scholar 

  27. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the Gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)

    Article  Google Scholar 

  28. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Netw. Learn. Syst. 26(5), 1048–1059 (2015)

    Article  MathSciNet  Google Scholar 

  29. Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the McDiarmid’s bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)

    Article  Google Scholar 

  30. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision trees for mining data streams. Inf. Sci. 266, 1–15 (2014)

    Article  Google Scholar 

  31. Serdah, A.M., Ashour, W.M.: Clustering large-scale data based on modified affinity propagation algorithm. J. Artif. Intell. Soft Comput. Res. 6(1), 23–33 (2016)

    Article  Google Scholar 

  32. Smola̧g, J., Bilski, J.: A systolic array for fast learning of neural networks. In: Proceedings of V Conference Neural Networks and Soft Computing, Zakopane, pp. 754–758 (2000)

    Google Scholar 

  33. Smola̧g, J., Rutkowski, L., Bilski, J.: Systolic array for neural networks. In: Proceedings of IV Conference Neural Networks and their Applications, Zakopane, pp. 487–497 (1999)

    Google Scholar 

  34. Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. (2015). doi:10.1007/s10044-015-0525-8

    Google Scholar 

  35. Tadeusiewicz, R.: Neural Networks. AOW RM (1993). (in Polish)

    Google Scholar 

  36. Werbos, J.: Backpropagation through time: what it does and how to do it. Proc. IEEE 78(10), 1550–1560 (1990)

    Article  Google Scholar 

  37. Wilamowski, B.M., Yo, H.: Neural network learning without backpropagation. IEEE Trans. Neural Netw. 21(11), 1793–1803 (2010)

    Article  Google Scholar 

  38. Wilamowski, B.M., Yo, H.: Improved computation for Levenberg-Marquardt training. IEEE Trans. Neural Netw. 21(6), 930–937 (2010)

    Article  Google Scholar 

  39. Yo, H., Reiner, P.D., Xie, T., Bartczak, T., Wilamowski, B.M.: An incremental design of radial basis function networks. IEEE Trans. Neural Netw. Learn. Syst. 25(10), 1793–1803 (2014)

    Article  Google Scholar 

  40. Zalasiński, M., Łapa, K., Cpałka, K.: New algorithm for evolutionary selection of the dynamic signature global features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS(LNAI), vol. 7895, pp. 113–121. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jarosław Bilski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Bilski, J., Galushkin, A.I. (2016). A New Proposition of the Activation Function for Significant Improvement of Neural Networks Performance. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39378-0_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39377-3

  • Online ISBN: 978-3-319-39378-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics