Skip to main content
Springer Nature Link
Log in

Fast Conjugate Gradient Algorithm for Feedforward Neural Networks

  • Conference paper
  • First Online:
Artificial Intelligence and Soft Computing (ICAISC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12415))

Included in the following conference series:

Abstract

The conjugate gradient (CG) algorithm is a method for learning neural networks. The highest computational load in this method is directional minimization. In this paper a new modification of the conjugate gradient algorithm is presented. The proposed solution speeds up the directional minimization, which result in a significant reduction of the calculation time. This modification of the CG algorithm was tested on selected examples. The performance of our method and the classic CG method was compared.

This work has been supported by the Polish National Science Center under Grant 2017/27/B/ST6/02852 and the program of the Polish Minister of Sciencea and higher Education under the name “Regional Initiative of Excellence” in the years 2019–2022 project number 020/RID/2018/19, the amount of financing PLN 12,000,000.00.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang, Z., Cao, J., Cai, Z., Rutkowski, L.: Anti-synchronization in fixed time for discontinuous reaction-diffusion neural networks with time-varying coefficients and time delay. IEEE Trans. Cybern. 50(6), 2758–2769 (2020). https://doi.org/10.1109/TCYB.2019.2913200

  2. Duda, P., Rutkowski, L., Jaworski, M., Rutkowska, D.: On the Parzen Kernel-based probability density function learning procedures over time-varying streaming data with applications to pattern classification. IEEE Trans. Cybern. 50(4), 1683–1696 (2020). https://doi.org/10.1109/TCYB.2018.2877611

  3. Lin, L., Cao, J., Rutkowski, L.: Robust event-triggered control invariance of probabilistic Boolean control networks. IEEE Trans. Neural Netw. Learn. Syst. 31(3), 1060–1065 (2020). https://doi.org/10.1109/TNNLS.2019.2917753

    Article  MathSciNet  Google Scholar 

  4. Liu, Y., Zheng, Y., Lu, J., Cao, J., Rutkowski, L.: Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans. Neural Netw. Learn. Syst. 31(3), 1022–1035 (2020). https://doi.org/10.1109/TNNLS.2019.2916597

    Article  MathSciNet  Google Scholar 

  5. Gabryel, M., Przybyszewski, K.: The dynamically modified BoW algorithm used in assessing clicks in online ads. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2019. LNCS (LNAI), vol. 11509, pp. 350–360. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20915-5_32

    Chapter  Google Scholar 

  6. Gabryel, M.: The bag-of-words method with different types of image features and dictionary analysis. J. Univ. Comput. Sci. 24(4), 357–371 (2018)

    MathSciNet  Google Scholar 

  7. Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. 20, 687–700 (2017)

    Article  MathSciNet  Google Scholar 

  8. Łapa, K., Cpałka, K., Wang, L.: New method for design of fuzzy systems for nonlinear modelling using different criteria of interpretability. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014. LNCS (LNAI), vol. 8467, pp. 217–232. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07173-2_20

    Chapter  Google Scholar 

  9. Zalasiński, M., Cpałka, K., Er, M.J.: New method for dynamic signature verification using hybrid partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014. LNCS (LNAI), vol. 8468, pp. 216–230. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07176-3_20

    Chapter  Google Scholar 

  10. Szczypta, J., Przybył, A., Cpałka, K.: Some aspects of evolutionary designing optimal controllers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7895, pp. 91–100. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38610-7_9

    Chapter  Google Scholar 

  11. Rutkowski, T., Romanowski, J., Woldan, P., Staszewski, P., Nielek, R., Rutkowski, L.: A content-based recommendation system using neuro-fuzzy approach. In: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–8 (2018)

    Google Scholar 

  12. Rutkowski, T., Łapa, K., Nowicki, R., Nielek, R., Grzanek, K.: On explainable recommender systems based on fuzzy rule generation techniques. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2019. LNCS (LNAI), vol. 11508, pp. 358–372. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20912-4_34

    Chapter  Google Scholar 

  13. Rutkowski, L.: Computational Intelligence. Methods and Techniques. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-76288-1

    Book  MATH  Google Scholar 

  14. Liao, J., Liu, T., Liu, M., Wang, J., Wang, Y., Sun, H.: Multi-context integrated deep neural network model for next location prediction. IEEE Access 6, 21980–21990 (2018)

    Google Scholar 

  15. Akdeniz, E., Egrioglu, E., Bas, E., Yolcu, U.: An ARMA type pi-sigma artificial neural network for nonlinear time series forecasting. J. Artif. Intell. Soft Comput. Res. 8(2), 121–132 (2017)

    Google Scholar 

  16. Nobukawa, S., Nishimura, H., Yamanishi, T.: Pattern classification by spiking neural networks combining self-organized and reward-related spike-timing-dependent plasticity. J. Artif. Intell. Soft Comput. Res. 9(4), 283–291 (2019)

    Article  Google Scholar 

  17. de Souza, G.B., da Silva Santos, D.F., Pires, R.G., Marananil, A.N., Papa, J.P.: Deep features extraction for robust fingerprint spoofing attack detection. J. Artif. Intell. Soft Comput. Res. 9(1), 41–49 (2019)

    Google Scholar 

  18. 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 

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

    Google Scholar 

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

    Article  Google Scholar 

  21. Bilski, J., Kowalczyk, B., Marchlewska, A., Zurada, J.M.: Local Levenberg-Marquardt algorithm for learning feedforwad neural networks. J. Artif. Intell. Soft Comput. Res. 10(4), 299–316 (2020). https://doi.org/10.2478/jaiscr-2020-0020

    Article  Google Scholar 

  22. Żurada, J.: Introduction to Artificial Neural Systems. West Publishing Co., Eagan (1992)

    Google Scholar 

  23. Liu, J.-B., Zhao, J., Wang, S., Javaid, M., Cao, J.: On the topological properties of the certain neural networks. J. Artif. Intell. Soft Comput. Res. 8(4), 257–268 (2018)

    Article  Google Scholar 

  24. Shewalkar, A., Nyavanandi, D., Ludwig, S., A.: Performance evaluation of deep neural networks applied to speech recognition: RNN, LSTM AND GRU. J. Artif. Intell. Soft Comput. Res. 9(4), 235–245 (2019)

    Google Scholar 

  25. Ludwig, S.A.: Applying a neural network ensemble to intrusion detection. J. Artif. Intell. Soft Comput. Res. 9(3), 177–188 (2019)

    Article  Google Scholar 

  26. 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). https://doi.org/10.1007/978-3-540-24844-6_19

    Chapter  Google Scholar 

  27. 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). https://doi.org/10.1007/978-3-540-69731-2_2

    Chapter  Google Scholar 

  28. 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. LNCS (LNAI), vol. 6114, pp. 19–25. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13232-2_3

    Chapter  Google Scholar 

  29. Bilski, J., Smoląg, 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. LNCS (LNAI), vol. 7267, pp. 12–20. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29347-4_2

    Chapter  Google Scholar 

  30. Bilski, J., Smoląg, 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. LNCS (LNAI), vol. 7267, pp. 12–20. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29347-4_2

    Chapter  Google Scholar 

  31. Bilski, J., Wilamowski, B.M.: Parallel Levenberg-Marquardt algorithm without error backpropagation. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10245, pp. 25–39. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59063-9_3

    Chapter  Google Scholar 

  32. Smoląg, J., Bilski, J.: A systolic array for fast learning of neural networks. In: Tenne, Y., Goh, C.K., (eds.) Proceedings of V Conference on Neural Networks and Soft Computing, Zakopane, pp. 754–758 (2000)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  36. 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 

  37. Werbos, J.: Backpropagation through time: what it does and how to do it. In: Proceedings of the IEEE, vol. 78, p. 10 (1990)

    Google Scholar 

  38. Charalambous, C.: Conjugate gradient algorithm for efficient training of artificial neural networks. IEE Proc. G Circuits Devices Syst. 139(3), 301–310 (1992)

    Article  Google Scholar 

  39. Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. Comput. J. 6, 163–168 (1963)

    Article  MathSciNet  Google Scholar 

  40. Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. Comput. J. 7, 149–154 (1964)

    Article  MathSciNet  Google Scholar 

  41. Nocedal, J., Wright, S.J.: Conjugate Gradient Methods in Numerical Optimization, pp. 497–528. Springer, New York (2006)

    Google Scholar 

  42. Polak, E.: Computational Methods in Optimization: A Unified Approach. Academic Press, New York (1971)

    Google Scholar 

  43. Navi, N.M.F., Ransing, M.R., Ransing, R.S.: An improved learning algorithm based on the conjugate gradient method for back propagation neural networks. Int. J. Comput. Inf. Eng. 2(8), 2770–2774 (2008)

    Google Scholar 

  44. Jin, X.-B., Zhang, X.-Y., Huang, K., Geng, G.-G.: Stochastic conjugate gradient algorithm with variance reduction. IEEE Trans. Neural Netw. Learn. Syst. 30(5), 1360–1369 (2019)

    Article  MathSciNet  Google Scholar 

  45. Rafajłowicz, E., Rafajłowicz, W.: Iterative learning in optimal control of linear dynamic processes. Int. J. Control 91(7), 1522–1540 (2018)

    Article  MathSciNet  Google Scholar 

  46. Rafajłowicz, E., Rafajłowicz, W.: Iterative learning in repetitive optimal control of linear dynamic processes. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9692, pp. 705–717. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39378-0_60

    Chapter  Google Scholar 

  47. Jurewicz, P., Rafajłowicz, W., Reiner, J., Rafajłowicz, E.: Simulations for tuning a laser power control system of the cladding process. In: Saeed, K., Homenda, W. (eds.) CISIM 2016. LNCS, vol. 9842, pp. 218–229. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45378-1_20

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Częstochowa University of Technology, al. Armii Krajowej 36, 42-200, Częstochowa, Poland

    Jarosław Bilski & Jacek Smoląg

Authors
  1. Jarosław Bilski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacek Smoląg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jarosław Bilski .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. Electrical and Computer Engineering, University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bilski, J., Smoląg, J. (2020). Fast Conjugate Gradient Algorithm for Feedforward Neural Networks. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2020. Lecture Notes in Computer Science(), vol 12415. Springer, Cham. https://doi.org/10.1007/978-3-030-61401-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-61401-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61400-3

  • Online ISBN: 978-3-030-61401-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics