Fast Computational Approach to the Levenberg-Marquardt Algorithm for Training Feedforward Neural Networks

[1] Marcin Gabryel, Dawid Lada, Zbigniew Filutowicz, Zofia Patora-Wysocka, Marek Kisiel-Dorohinicki, and Guang Yi Chen. Detecting anomalies in advertising web traffic with the use of the variational autoencoder. Journal of Artificial Intelligence and Soft Computing Research, 12(4):255–256, 2022.10.2478/jaiscr-2022-0017 Search in Google Scholar

[2] Marcin Zalasiński, Łukasz Laskowski, Tacjana Niksa-Rynkiewicz, Krzysztof Cpałka, Alek-sander Byrski, Krzysztof Przybyszewski, Paweł Trippner, and Shi Dong. Evolutionary algorithm for selecting dynamic signatures partitioning approach. Journal of Artificial Intelligence and Soft Computing Research, 12(4):267–279, 2022.10.2478/jaiscr-2022-0018 Search in Google Scholar

[3] S. Albawi, T. A. Mohammed, and S. Al-Zawi. Understanding of a convolutional neural network. In 2017 International Conference on Engineering and Technology (ICET), pages 1–6, 2017.10.1109/ICEngTechnol.2017.8308186 Search in Google Scholar

[4] A. M. Taqi, A. Awad, F. Al-Azzo, and M. Milanova. The impact of multi-optimizers and data augmentation on tensorflow convolutional neural network performance. In 2018 IEEE Conference on Multimedia Information Processing and Retrieval (MIPR), pages 140–145, April 2018.10.1109/MIPR.2018.00032 Search in Google Scholar

[5] Jiuxiang Gu, Zhenhua Wang, Jason Kuen, Lianyang Ma, Amir Shahroudy, Bing Shuai, Ting Liu, Xingxing Wang, Gang Wang, Jianfei Cai, and Tsuhan Chen. Recent advances in convolutional neural networks. Pattern Recognition, 77:354 – 377, 2018.10.1016/j.patcog.2017.10.013 Search in Google Scholar

[6] Robert K. Nowicki and Janusz T. Starczewski. A new method for classification of imprecise data using fuzzy rough fuzzification. Inf. Sci., 414:33–52, 2017.10.1016/j.ins.2017.05.049 Search in Google Scholar

[7] Janusz T. Starczewski, Katarzyna Nieszporek, Michal Wróbel, and Konrad Grzanek. A fuzzy SOM for understanding incomplete 3d faces. In ICAISC (2), volume 10842 of Lecture Notes in Computer Science, pages 73–80. Springer, 2018.10.1007/978-3-319-91262-2_7 Search in Google Scholar

[8] Michal Wróbel, Katarzyna Nieszporek, Janusz T. Starczewski, and Andrzej Cader. A fuzzy measure for recognition of handwritten letter strokes. In ICAISC (1), volume 10841 of Lecture Notes in Computer Science, pages 761–770. Springer, 2018.10.1007/978-3-319-91253-0_70 Search in Google Scholar

[9] Jarosław Bilski, Bartosz Kowalczyk, Alina Marchlewska, and Jacek M. Zurada. Local levenberg-marquardt algorithm for learning feedforwad neural networks. Journal of Artificial Intelligence and Soft Computing Research, 10(4):299–316, 2020.10.2478/jaiscr-2020-0020 Search in Google Scholar

[10] Jarosław Bilski, Bartosz Kowalczyk, Andrzej Marjański, Michał Gandor, and Jacek Zurada. A novel fast feedforward neural networks training algorithm. Journal of Artificial Intelligence and Soft Computing Research, 11(4):287–306, 2021.10.2478/jaiscr-2021-0017 Search in Google Scholar

[11] Jarosław Bilski, Bartosz Kowalczyk, Marek Kisiel-Dorohinicki, Agnieszka Siwocha, and Jacek Żurada. Towards a very fast feedforward multilayer neural networks training algorithm. Journal of Artificial Intelligence and Soft Computing Research, 12(3):181–195, 2022.10.2478/jaiscr-2022-0012 Search in Google Scholar

[12] Xin Wang, Yi Guo, Yuanyuan Wang, and Jinhua Yu. Automatic breast tumor detection in abvs images based on convolutional neural network and superpixel patterns. Neural Computing and Applications, 31(4):1069–1081, 2019.10.1007/s00521-017-3138-x Search in Google Scholar

[13] Muhammad Irfan Sharif, Jian Ping Li, Muhammad Attique Khan, and Muhammad Asim Saleem. Active deep neural network features selection for segmentation and recognition of brain tumors using mri images. Pattern Recognition Letters, 129:181 – 189, 2020.10.1016/j.patrec.2019.11.019 Search in Google Scholar

[14] P. Mohamed Shakeel, T. E. E. Tobely, H. Al-Feel, G. Manogaran, and S. Baskar. Neural network based brain tumor detection using wireless infrared imaging sensor. IEEE Access, 7:5577–5588, 2019.10.1109/ACCESS.2018.2883957 Search in Google Scholar

[15] Alexander Rakhlin, Alexey Shvets, Vladimir Iglovikov, and Alexandr A. Kalinin. Deep convolutional neural networks for breast cancer histology image analysis. In Aurélio Campilho, Fakhri Karray, and Bart ter Haar Romeny, editors, Image Analysis and Recognition, pages 737–744, Cham, 2018. Springer International Publishing.10.1007/978-3-319-93000-8_83 Search in Google Scholar

[16] Xin Cai, Yufeng Qian, Qingshan Bai, and Wei Liu. Exploration on the financing risks of enterprise supply chain using back propagation neural network. Journal of Computational and Applied Mathematics, 367:112457, 2020.10.1016/j.cam.2019.112457 Search in Google Scholar

[17] Amin Hedayati Moghaddam, Moein Hedayati Moghaddam, and Morteza Esfandyari. Stock market index prediction using artificial neural network. Journal of Economics, Finance and Administrative Science, 21(41):89 – 93, 2016.10.1016/j.jefas.2016.07.002 Search in Google Scholar

[18] Songqiao Qi, Kaijun Jin, Baisong Li, and Yufeng Qian. The exploration of internet finance by using neural network. Journal of Computational and Applied Mathematics, 369:112630, 2020.10.1016/j.cam.2019.112630 Search in Google Scholar

[19] A. V. Kurbesov, D. V. Ryabkin, I. I. Miroshnichenko, N. A. Aruchidi, and K. Kh. Kalugyan. Automated voice recognition of emotions through the use of neural networks. In Rafik A. Aliev, Janusz Kacprzyk, Witold Pedrycz, Mo Jamshidi, Mustafa B. Babanli, and Fahreddin M. Sadikoglu, editors, 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019, pages 675–682, Cham, 2020. Springer International Publishing.10.1007/978-3-030-35249-3_87 Search in Google Scholar

[20] X. Changzhen, W. Cong, M. Weixin, and S. Yanmei. A traffic sign detection algorithm based on deep convolutional neural network. In 2016 IEEE International Conference on Signal and Image Processing (ICSIP), pages 676–679, Aug 2016.10.1109/SIPROCESS.2016.7888348 Search in Google Scholar

[21] Katsuba Yurii and Grigorieva Liudmila. Application of artificial neural networks in vehicles’ design self-diagnostic systems for safety reasons. Transportation Research Procedia, 20:283 – 287, 2017. 12th International Conference ”Organization and Traffic Safety Management in large cities SPbOTSIC-2016, 28-30 September 2016, St. Petersburg, Russia.10.1016/j.trpro.2017.01.024 Search in Google Scholar

[22] N. P. Patel and A. Kale. Optimize approach to voice recognition using iot. In 2018 International Conference On Advances in Communication and Computing Technology (ICACCT), pages 251–256, 2018.10.1109/ICACCT.2018.8529622 Search in Google Scholar

[23] Yi Mou and Kun Xu. The media inequality: Comparing the initial human-human and human-ai social interactions. Computers in Human Behavior, 72:432 – 440, 2017. Search in Google Scholar

[24] Werbos J. Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Harvard University, 1974. Search in Google Scholar

[25] Scott E. Fahlman. An empirical study of learning speed in back-propagation networks. Technical report, 1988. Search in Google Scholar

[26] M. Riedmiller and H. Braun. A direct adaptive method for faster backpropagation learning: the rprop algorithm. In IEEE International Conference on Neural Networks, pages 586–591 vol.1, March 1993. Search in Google Scholar

[27] Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In Proceedings of the 30th International Conference on International Conference on Machine Learning - Volume 28, ICML’13, pages III– 1139–III–1147. JMLR.org, 2013. Search in Google Scholar

[28] M. T. Hagan and M.B. Menhaj. Training feedforward networks with the marquardt algorithm. IEEE Transactions on Neuralnetworks, 5:989–993, 1994.10.1109/72.32969718267874 Search in Google Scholar

[29] N. Ampazis and S. J. Perantonis. Two highly efficient second-order algorithms for training feedforward networks. IEEE Transactions on Neural Networks, 13(5):1064–1074, 2002.10.1109/TNN.2002.103193918244504 Search in Google Scholar

[30] J. S. Smith, B. Wu, and B. M. Wilamowski. Neural network training with Levenberg–Marquardt and adaptable weight compression. IEEE Transactions on Neural Networks and Learning Systems, 30(2):580–587, 2019.10.1109/TNNLS.2018.284677529994621 Search in Google Scholar

[31] Miao Cui, Kai Yang, Xiao liang Xu, Sheng dong Wang, and Xiao wei Gao. A modified Levenberg–Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems. International Journal of Heat and Mass Transfer, 97:908 – 916, 2016.10.1016/j.ijheatmasstransfer.2016.02.085 Search in Google Scholar

[32] Jiyang Dong, Ke Lu, Jian Xue, Shuangfeng Dai, Rui Zhai, and Weiguo Pan. Accelerated nonrigid image registration using improved Levenberg–Marquardt method. Information Sciences, 423:66 – 79, 2018.10.1016/j.ins.2017.09.059 Search in Google Scholar

[33] Jarosław Bilski, Bartosz Kowalczyk, and Jacek M. Żurada. 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, pages 46–56. Springer-Verlag Berlin Heidelberg, 2016.10.1007/978-3-319-39378-0_5 Search in Google Scholar

[34] Jacek Smoląg, Jarosław Bilski, and Leszek Rutkowski. Systolic array for neural networks. In IV KSNiIZ, pages 487–497, 1999. Search in Google Scholar

[35] Jacek Smoląg and Jarosław Bilski. A systolic array for fast learning of neural networks. In V NNSC, pages 754–758, 2000. Search in Google Scholar

[36] D. Rutkowska, R.K. Nowicki, and Y. Hayashi. Parallel processing by implication-based neuro–fuzzy systems. Lecture Notes in Computer Science, 2328:599–607, 2002.10.1007/3-540-48086-2_66 Search in Google Scholar

[37] Jarosław Bilski and Jacek Smoląg. Parallel realisation of the recurrent RTRN neural network learning. In Artificial Intelligence and Soft Computing, volume 5097 of Lecture Notes in Computer Science, pages 11–16. Springer-Verlag Berlin Heidelberg, 2008.10.1007/978-3-540-69731-2_2 Search in Google Scholar

[38] Jarosław Bilski and Jacek Smoląg. Parallel architectures for learning the RTRN and Elman dynamic neural network. IEEE Transactions on Parallel and Distributed Systems, 26(9):2561 – 2570, 2015.10.1109/TPDS.2014.2357019 Search in Google Scholar

[39] Jarosław Bilski, Jacek Smoląg, and Jacek M. Żurada. Parallel approach to the Levenberg-Marquardt learning algorithm for feedforward neural networks. In Artificial Intelligence and Soft Computing, volume 9119 of Lecture Notes in Computer Science, pages 3–14. Springer-Verlag Berlin Heidelberg, 2015.10.1007/978-3-319-19324-3_1 Search in Google Scholar

[40] J. Bilski and B.M. Wilamowski. Parallel Levenberg-Marquardt algorithm without error backpropagation. Artificial Intelligence and Soft Computing, Springer-Verlag Berlin Heidelberg, LNAI 10245:25–39, 2017.10.1007/978-3-319-59063-9_3 Search in Google Scholar