Abstract
This paper presents an application of the scaled Givens rotations in the process of feedforward artificial neural networks training. This method bases on the QR decomposition. The paper describes mathematical background that needs to be considered during the application of the scaled Givens rotations in neural networks training. The paper concludes with sample simulation results.
This work has been supported by the Polish National Science Center under Grant 2017/27/B/ST6/02852.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bilski, J.: Momentum modification of the RLS algorithms. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 151–157. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24844-6_18
Bilski, J.: Parallel structures for feedforward and dynamic neural networks. (In Polish) Akademicka Oficyna Wydawnicza EXIT (2013)
Bilski, J., Kowalczyk, B., Grzanek, K.: The parallel modification to the Levenberg-Marquardt algorithm. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2018. LNCS (LNAI), vol. 10841, pp. 15–24. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91253-0_2
Bilski,, J., Kowalczyk, B., Żurada, J.M.: Application of the Givens rotations in the neural network learning algorithm. In: Artificial Intelligence and Soft Computing, volume 9602 of Lecture Notes in Artificial Intelligence, pp. 46–56. Springer-Verlag, Berlin, Heidelberg (2016). https://doi.org/10.1007/978-3-319-39378-0_5
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.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10245, pp. 14–24. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59063-9_2
Bilski, J., Smoląg, J.: Parallel realisation of the recurrent multi layer perceptron learning. Artificial Intelligence and Soft Computing, pp. 12–20. Springer-Verlag, Berlin, Heidelberg, (LNAI 7267) (2012). https://doi.org/10.1007/978-3-642-13232-2_3
Bilski, J., Smoląg, J.: Parallel approach to learning of the recurrent Jordan neural network. Artificial Intelligence and Soft Computing, pp. 32–40. Springer-Verlag, Berlin, Heidelberg (LNAI 7895) (2013)
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)
Bilski, J., Smoląg, J., Galushkin, A.I.: The parallel approach to the conjugate gradient learning algorithm for the feedforward neural networks. In: Artificial Intelligence and Soft Computing, volume 8467 of Lecture Notes in Computer Science, pp. 12–21. Springer-Verlag, Berlin, Heidelberg (2014). https://doi.org/10.1007/978-3-319-07173-2_2
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.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 3–14. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19324-3_1
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)
Cao, Y., Samidurai, R., Sriraman, R.: Stability and dissipativity analysis for neutral type stochastic markovian jump static neural networks with time delays. J. Artif. Intell. Soft Comput. Res. 9(3), 189–204 (2019)
Costa, M., Oliveira, D., Pinto, S., Tavares, A.: Detecting driver’s fatigue, distraction and activity using a non-intrusive AI-based monitoring system. J. Artif. Intell. Soft Comput. Rese. 9(4), 247–266 (2019)
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)
Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)
Duda, P., Jaworski, M., Cader, A., Wang, L.: On training deep neural networks using a streaming approach. J. Artif. Intell. Soft Computi. Res. 10(1), 15–26 (2020)
Gabryel, M., Grzanek, K., Hayashi, Y.: Browser fingerprint coding methods increasing the effectiveness of user identification in the web traffic. J. Artif. Intell. Soft Computi. Res. 10(4), 243–253 (2020)
Gentleman, W.M.: Least squares computations by givens transformations without square roots. IMA J. Appl. Math. 12(3), 329–336 (1973)
Givens, W.: Computation of plain unitary rotations transforming a general matrix to triangular form. J. Soc. Indust. Appl. Math. 6, 26–50 (1958)
Grycuk, R., Najgebauer, P., Kordos, M., Scherer, M.M., Marchlewska, A.: Fast image index for database management engines. J. Artif. Intell. Soft Computi. Res. 10(2), 113–123 (2020)
Grycuk, R., Wojciechowski, A., Wei, W., Siwocha, A.: Detecting visual objects by edge crawling. J. Artif. Intell. Soft Computi. Res. 10(3), 223–237 (2020)
Hagan, M.T., Menhaj, M.B.: Training feedforward networks with the marquardt algorithm. IEEE Trans. Neuralnetw. 5, 989–993 (1994)
Hou, Y., Holder, L.B.: On graph mining with deep learning: introducing model r for link weight prediction. J. Artif. Intell. Soft Computi. Res. 9(1), 21–40 (2019)
Kamimura, R.: Supposed maximum mutual information for improving generalization and interpretation of multi-layered neural networks. J. Artif. Intell. Soft Computi. Res. 9(2), 123–147 (2019)
Kiełbasiński, A., Schwetlick, H.: Numeryczna Algebra Liniowa: Wprowadzenie do Obliczeń Zautomatyzowanych. Wydawnictwa Naukowo-Techniczne, Warszawa (1992)
Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization (2014)
Krell, E., Sheta, A., Balasubramanian, A.P.R., King, S.A.: Collision-free autonomous robot navigation in unknown environments utilizing pso for path planning. J. Artif. Intell. Soft Comput. Res. 9(4), 267–282 (2019)
Kumarratneshk, R., Weilleweill, E., Aghdasi, F., Sriram, P.: A strong and efficient baseline for vehicle re-identification using deep triplet embedding. J. Artif. Intell. Soft Comput. Res. 10(1), 27–45 (2020)
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., Rafał Scherer, R., Tadeusiewicz, L.A.Z., Zurada, J.M. (eds.) Artificial Intelligence and Soft Computing, pp. 217–232. Springer International Publishing, Cham (2014). https://doi.org/10.1007/978-3-319-07173-2_20
Ludwig, S.A.: Applying a neural network ensemble to intrusion detection. J. Artif. Intell. Soft Comput. Res. 9(3), 177–188 (2019)
Abbas, M. Javaid, M., Jia-Bao, L., Teh, W.C., Jinde, C.: Topological properties of four-layered neural networks. J. Artif. Intell. Soft Comput. Res. 9(2), 111–122 (2019)
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)
Nowicki, R.K., Grzanek, K., Hayashi, Y.: Rough support vector machine for classification with interval and incomplete data. J. Artif. Intell. Soft Comput. Res. 10(1), 47–56 (2020)
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)
Simões, D., Lau, N., Reis, L.P.: Multi agent deep learning with cooperative communication. J. Artif. Intell. Soft Comput. Res. 10(3), 189–207 (2020)
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
Wei, Y., Ying, Yu., Lifeng, X., Huang, W., Guo, J., Wan, Y., Cao, J.: Vehicle emission computation through microscopic traffic simulation calibrated using genetic algorithm. J. Artif. Intell. Soft Comput. Res. 9(1), 67–80 (2019)
Werbos, J.: Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Harvard University (1974)
Zalasiński, M., Cpałka, K., Er, M.J.: New method for dynamic signature verification using hybrid partitioning. In: Rutkowski, L., Korytkowski, M., Rafał Scherer, R., Tadeusiewicz, L.A.Z., Zurada, J.M. (eds.) Artificial Intelligence and Soft Computing, pp. 216–230. Springer International Publishing, Cham (2014). https://doi.org/10.1007/978-3-319-07176-3_20
Zeiler, M.D.: An adaptive learning rate method, Adadelta (2012)
Zhao, X., Song, M., Liu, A., Wang, Y., Wang, T., Cao, J.: Data-driven temporal-spatial model for the prediction of AQI in nanjing. J. Artif. Intell. Soft Comput. Res. 10(4), 255–270 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Bilski, J., Kowalczyk, B. (2021). A New Variant of the GQR Algorithm for Feedforward Neural Networks Training. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2021. Lecture Notes in Computer Science(), vol 12854. Springer, Cham. https://doi.org/10.1007/978-3-030-87986-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-87986-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87985-3
Online ISBN: 978-3-030-87986-0
eBook Packages: Computer ScienceComputer Science (R0)