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Enhancing the Levenberg-Marquardt Method in Neural Network training using the direct computation of the Error Cost Function Hessian

Published: 25 September 2015 Publication History

Abstract

The Levenberg-Marquardt (LM) algorithm is a very popular training method in Neural Networks due to its accuracy and robustness. LM outperforms gradient based methods that use direct calculation of the first derivative of the error cost function through back-propagation. In this paper we will examine how the direct computation of the diagonal elements of the Hessian matrix of the error cost function can be used to improve the performance of the original LM algorithm.

References

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R. Battiti, "First- and Second-Order Methods for Learning: Between Steepest Descent and Newton's Method," Neural Computation, vol. 4, no. 2, pp. 141--266, 1992.
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K. Levenberg, "A Method for the Solution of Certain Non-Linear Problems in Least Squares," Quarterly of Applied Mathematics, vol. 2, no. 2, pp. 164--168, 1944.
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J. Peng, K. Li and G. Irwin, "A new Jacobian matrix for optimal learning of single-layer neural networks," IEEE Trans Neural Netw, vol. 19, no. 1, pp. 119--29, 2008.
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Y.-T. Kwak and J. Heesung, "A Layer-by-Layer Levenberg-Marquardt algorithm for Feedforward Multilayer Perceptron," Applied Mathematics & Information Sciences, vol. 6, pp. 505--511, 2011.
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Y. A. LeCun, L. Bottou, G. B. Orr and K.-R. Muller, "Efficient BackProp," in Neural Networks: Tricks of the trade, Springer, 1998, pp. 9--47.
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G. Tesauro and B. Janssens, "Scaling Relationships in Back-propagation Learninng," Complex Systems, vol. 2, pp. 39--44, 1988.
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K. J. Lang and M. J. Witbrock, "Learning to Tell Two Spirals Apart," in In Proceeding of the Connectioninst Models Summer School, 1988.

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  1. Enhancing the Levenberg-Marquardt Method in Neural Network training using the direct computation of the Error Cost Function Hessian

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        cover image ACM Other conferences
        EANN '15: Proceedings of the 16th International Conference on Engineering Applications of Neural Networks (INNS)
        September 2015
        266 pages
        ISBN:9781450335805
        DOI:10.1145/2797143
        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        In-Cooperation

        • Aristotle University of Thessaloniki
        • INNS: International Neural Network Society

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        Published: 25 September 2015

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        Author Tags

        1. Levenberg-Marquardt
        2. Neural Networks
        3. Second Order Gradient Methods

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        16th EANN workshops

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        EANN '15 Paper Acceptance Rate 36 of 60 submissions, 60%;
        Overall Acceptance Rate 36 of 60 submissions, 60%

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        • (2024)Prediction of In-vitro Dissolution Profile for Oral Dispersible Film (ODF) using Artificial Neural Network2024 IEEE 22nd Student Conference on Research and Development (SCOReD)10.1109/SCOReD64708.2024.10872643(192-196)Online publication date: 19-Dec-2024
        • (2019)WLI Fuzzy Clustering and Adaptive Lion Neural Network (ALNN) for Cloud Intrusion DetectionInternational Journal of Distributed Artificial Intelligence10.4018/IJDAI.201901010111:1(1-17)Online publication date: 1-Jan-2019
        • (2016)Chebyshev Multilayer Perceptron Neural Network with Levenberg Marquardt-Back Propagation Learning for Classification TasksRecent Advances on Soft Computing and Data Mining10.1007/978-3-319-51281-5_17(162-170)Online publication date: 29-Dec-2016

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