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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Stability Analysis of the Modified Levenberg–Marquardt Algorithm for the Artificial Neural Network Training
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Stability Analysis of the Modified Levenberg–Marquardt Algorithm for the Artificial Neural Network Training

机译：改进的Levenberg-Marquardt算法对人工神经网络训练的稳定性分析

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摘要

The Levenberg-Marquardt and Newton are two algorithms that use the Hessian for the artificial neural network learning. In this article, we propose a modified Levenberg-Marquardt algorithm for the artificial neural network learning containing the training and testing stages. The modified Levenberg-Marquardt algorithm is based on the Levenberg-Marquardt and Newton algorithms but with the following two differences to assure the error stability and weights boundedness: 1) there is a singularity point in the learning rates of the Levenberg-Marquardt and Newton algorithms, while there is not a singularity point in the learning rate of the modified Levenberg-Marquardt algorithm and 2) the Levenberg-Marquardt and Newton algorithms have three different learning rates, while the modified Levenberg-Marquardt algorithm only has one learning rate. The error stability and weights boundedness of the modified Levenberg-Marquardt algorithm are assured based on the Lyapunov technique. We compare the artificial neural network learning with the modified Levenberg-Marquardt, Levenberg-Marquardt, Newton, and stable gradient algorithms for the learning of the electric and brain signals data set.
机译：Levenberg-Marquardt和Newton是两种使用Hessian的人工神经网络学习的算法。在本文中，我们提出了一种改进的Levenberg-Marquardt算法，用于含有培训和测试阶段的人工神经网络学习。修改的Levenberg-Marquardt算法基于Levenberg-Marquardt和Newton算法，但随着以下两种差异，以确保错误稳定性和重量有界限：1）Levenberg-Marquardt和牛顿算法的学习率有一个奇点点，虽然没有修改的Levenberg-Marquardt算法的学习率的奇点点，但是Levenberg-Marquardt和牛顿算法有三种不同的学习速率，而改进的Levenberg-Marquardt算法只有一种学习率。基于Lyapunov技术，确保了改进的Levenberg-Marquardt算法的误差稳定性和重量界限。我们将人工神经网络学习与改进的Levenberg-Marquardt，Levenberg-Marquardt，Newton和稳定的梯度算法进行比较，以及用于学习电动和脑信号数据集的稳定梯度算法。

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