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Three-Dimensional Model of Signal Processing in the Presynaptic Bouton of the Neuron Read chapter Read first chapter

2018 | OriginalPaper | Chapter

The Parallel Modification to the Levenberg-Marquardt Algorithm

Authors : Jarosław Bilski, Bartosz Kowalczyk, Konrad Grzanek

Published in: Artificial Intelligence and Soft Computing

Publisher: Springer International Publishing

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Abstract

The paper presents a parallel approach to the Levenberg-Marquardt algorithm (also called LM or LMA). The first section contains the mathematical basics of the classic LMA. Then the parallel modification to LMA is introduced. The classic Levenberg-Marquardt algorithm is sufficient for a training of small neural networks. For bigger networks the algorithm complexity becomes too big for the effective teaching. The main scope of this paper is to propose more complexity efficient approach to LMA by parallel computation. The proposed modification to LMA has been tested on a few function approximation problems and has been compared to the classic LMA. The paper concludes with the resolution that the parallel modification to LMA could significantly improve algorithm performance for bigger networks. Summary also contains a several proposals for the possible future work directions in the considered area.

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Literature
1.
2.
Starczewski, A., Krzyżak, A.: Improvement of the validity index for determination of an appropriate data partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10246, pp. 159–170. Springer, Cham (2017). https://​doi.​org/​10.​1007/​978-3-319-59060-8_​16CrossRef
3.
4.
Bilski, J., Kowalczyk, B., Żurada, J.M.: Parallel implementation of the givens rotations in the neural network learning algorithm. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10245, pp. 14–24. Springer, Cham (2017). https://​doi.​org/​10.​1007/​978-3-319-59063-9_​2CrossRef
5.
6.
Bilski, J., Smoląg, J.: Parallel architectures for learning the rtrn and elman dynamic neural network. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561–2570 (2015)CrossRef
7.
Bilski, J., Smoląg, 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., Zurada, J. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 3–14. Springer, Cham (2015). https://​doi.​org/​10.​1007/​978-3-319-19324-3_​1MATHCrossRef
8.
Marqardt, D.: An algorithm for last-sqares estimation of nonlinear paeameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)CrossRef
9.
Hagan, M.T., Menhaj, M.B.: Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw. 5(6), 989–993 (1994)CrossRef
10.
Werbos, J.: Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Harvard University, Cambridge (1974)
11.
Cpałka, K., Łapa, K., Przybył, A.: A new approach to design of control systems using genetic programming. Inf. Technol. Control 44(4), 433–442 (2015)
12.
Łapa, K., Cpałka, K.: On the application of a hybrid genetic-firework algorithm for controllers structure and parameters selection. In: Borzemski, L., Grzech, A., Świątek, J., Wilimowska, Z. (eds.) Information Systems Architecture and Technology: Proceedings of 36th International Conference on Information Systems Architecture and Technology – ISAT 2015 – Part I. AISC, vol. 429, pp. 111–123. Springer, Cham (2016). https://​doi.​org/​10.​1007/​978-3-319-28555-9_​10CrossRef
13.
Łapa, K., Cpałka, K., Galushkin, A.I.: A new interpretability criteria for neuro-fuzzy systems for nonlinear classification. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 448–468. Springer, Cham (2015). https://​doi.​org/​10.​1007/​978-3-319-19324-3_​41CrossRef
14.
Khan, N.A., Shaikh, A.: A smart amalgamation of spectral neural algorithm for nonlinear Lane-Emden equations with simulated annealing. J. Artif. Intell. Soft Comput. Res. 7(3), 215–224 (2017)CrossRef
15.
Liu, H., Gegov, A., Cocea, M.: Rule based networks: an efficient and interpretable representation of computational models. J. Artif. Intell. Soft Comput. Res. 7(2), 111–123 (2017)CrossRef
16.
Notomista, G., Botsch, M.: A machine learning approach for the segmentation of driving Maneuvers and its application in autonomous parking. J. Artif. Intell. Soft Comput. Res. 7(4), 243–255 (2017)CrossRef
17.
Rotar, C., Lantovics, L.B.: Directed evolution - a new Metaheuristc for optimization. J. Artif. Intell. Soft Comput. Res. 7(3), 183–200 (2017)CrossRef
18.
19.
Smoląg, J., Bilski, J.: A systolic array for fast learning of neural networks. In: V NNSC, pp. 754–758 (2000)
20.
Smoląg, J., Bilski, J., Rutkowski, L.: Systolic array for neural networks. In: IV KSNiIZ, pp. 487–497 (1999)
21.
Villmann, T., Bohnsack, A., Kaden, M.: Can learning vector quantization be an alternative to SVM and deep learning? Recent trends and advanced variants of learning vector quantization for classification learning. J. Artif. Intell. Soft Comput. Res. 7(1), 65–81 (2017)CrossRef
Metadata
Title
The Parallel Modification to the Levenberg-Marquardt Algorithm
Authors
Jarosław Bilski
Bartosz Kowalczyk
Konrad Grzanek
Copyright Year
2018
Book
Artificial Intelligence and Soft Computing

Print ISBN: 978-3-319-91252-3

Electronic ISBN: 978-3-319-91253-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91253-0_2

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