scholarly journals Estimation of Navigation Mark Floating Based on Fractional-Order Gradient Descent with Momentum for RBF Neural Network

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qionglin Fang
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Gradient Descent ◽  
Rbf Neural Network ◽  
Error Function ◽  
Initial Position ◽  
Descent Method ◽  
Local Optimum ◽  
Gradient Descent Method ◽  
The Neural Network

To address the difficulty of estimating the drift of the navigation marks, a fractional-order gradient with the momentum RBF neural network (FOGDM-RBF) is designed. The convergence is proved, and it is used to estimate the drifting trajectory of the navigation marks with different geographical locations. First, the weight of the neural network is set. The navigation mark’s meteorological, hydrological, and initial position data are taken as the input of the neural network. The neural network is trained and used to estimate the mark’s position. The navigation mark’s position is taken at a later time as the output of the neural network. The difference between the later position and the estimated position obtained from the neural network is the error function of the neural network. The influence of sea conditions and months are analyzed. The experimental results and error analysis show that FOGDM-RBF is better than other algorithms at trajectory estimation and interpolation, has better accuracy and generalization, and does not easily fall into the local optimum. It is effective at accelerating convergence speed and improving the performance of a gradient descent method.

scholarly journals The Power Cepstrum Calculation with Convolutional Neural Networks

2019 ◽  
Vol 19 (2) ◽  
pp. e13 ◽  
Author(s):  
Mario Alejandro García ◽  
Eduardo Atilio Destéfanis
Keyword(s):  
Neural Network ◽  
Fourier Transform ◽  
Gradient Descent ◽  
Descent Method ◽  
Intermediate Step ◽  
Gradient Descent Method ◽  
The Neural Network ◽  
Regression Problems ◽  
The One ◽  
Deep Learning Model

A model of neural network with convolutional layers that calculates the power cepstrum of the input signal is proposed. To achieve it, the network calculates the discrete-time short-term Fourier transform internally, obtaining the spectrogram of the signal as an intermediate step. The weights of the neural network can be calculated in a direct way or they can be obtained through training with the gradient descent method. The behaviour of the training is analysed. The model originally proposed cannot be trained in a complete way, but both the part that calculates the spectrogram and also a variant of the cepstrum equivalent to the autocovariance that keeps a big part of its usefulness can be trained. For the cases of successful training, an analysis of the obtained weights is done. The main conclusions indicate, on the one hand, that it is possible to calculate the power cepstrum with a neural network; on the other hand, that it is possible to use these networks as the initial layers of a deep learning model for the case of trainable models. In these layers, weights are initialised with the discrete Fourier transform (DFT) coefficients and they are trained to adapt to specific classification or regression problems.

scholarly journals Fractional-Order Deep Backpropagation Neural Network

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Chunhui Bao ◽  
Yifei Pu ◽  
Yi Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Bp Neural Network ◽  
Gradient Descent ◽  
Necessary Conditions ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Backpropagation Neural Network ◽  
Bp Neural Network Model

In recent years, the research of artificial neural networks based on fractional calculus has attracted much attention. In this paper, we proposed a fractional-order deep backpropagation (BP) neural network model with L2 regularization. The proposed network was optimized by the fractional gradient descent method with Caputo derivative. We also illustrated the necessary conditions for the convergence of the proposed network. The influence of L2 regularization on the convergence was analyzed with the fractional-order variational method. The experiments have been performed on the MNIST dataset to demonstrate that the proposed network was deterministically convergent and can effectively avoid overfitting.

scholarly journals RBF Neural Network-Based Frequency Band Prediction for Future Frequency Hopping Communications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Shengyan Zhu ◽  
Yongjian Wang ◽  
Jianbo Zheng ◽  
Shupeng Wang
Keyword(s):  
Neural Network ◽  
Frequency Band ◽  
Prediction Accuracy ◽  
Gradient Descent ◽  
Rbf Neural Network ◽  
Frequency Hopping ◽  
Descent Method ◽  
Signal Frequency ◽  
Gradient Descent Method ◽  
Swarm Optimization

On the basis of the chaotic features of the frequency hopping signal, frequency band prediction for frequency hopping signal can enhance the interference effect of the signal greatly. However, poor prediction accuracy often limits its development in the military field. Therefore, for the sake of enhancing the frequency band prediction accuracy of frequency hopping signal, this paper studies the radial basis function (RBF) neural network frequency hopping signal frequency band prediction model based on the gradient descent method and improved the particle swarm optimization algorithm, respectively. The former uses a step-by-step algorithm to optimize the center value and weight so that the network can find the most suitable initial state. Then, the clustering selection optimization algorithm is employed to optimize the central value. In addition, it optimizes the weight by using a gradient descent method of the optimal learning rate. The latter optimizes the structure of the RBF neural network through the combination of the subtractive clustering algorithm and improved the particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the gradient RBF algorithm model performs better in terms of accuracy, but time efficiency is lower, while the PSO-RBF algorithm has better time efficiency.

scholarly journals Model Predictive Control of Nonlinear System Based on GA-RBP Neural Network and Improved Gradient Descent Method

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Youming Wang ◽  
Didi Qing
Keyword(s):  
Neural Network ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Bp Neural Network ◽  
Gradient Descent ◽  
Tracking Error ◽  
Hessian Matrix ◽  
Descent Method ◽  
Local Optimum ◽  
Gradient Descent Method

A model predictive control (MPC) method based on recursive backpropagation (RBP) neural network and genetic algorithm (GA) is proposed for a class of nonlinear systems with time delays and uncertainties. In the offline modeling stage, a multistep-ahead predictor with GA-RBP neural network is designed, where GA-BP neural network is used as a one-step prediction model and GA is employed to train the initial weights and bias of the BP neural network. The incorporation of GA into RBP can reduce the possibility of the BP neural network falling into a local optimum instead of reaching global optimization. In the online optimizing stage, a multistep-ahead GA-RBP neural network predictor and an improved gradient descent method (IGDM) are proposed to efficiently solve the online optimization problem of nonlinear MPC by minimizing a modified quadratic criterion. The designed MPC strategy can avoid information loss while linearizing the controlled system and computing the Hessian matrix and its inverse matrix. Experimental results show that the proposed approach can reduce the computational burden and improve the performance of MPC (i.e., the maximum overshoots, calculation time, rise time, and RMSE tracking error value) for the solution of nonlinear controlled systems.

scholarly journals ANN based method for improving gold price forecasting accuracy through modified gradient descent methods

2020 ◽  
Vol 9 (1) ◽  
pp. 46
Author(s):  
Shilpa Verma ◽  
G. T. Thampi ◽  
Madhuri Rao
Keyword(s):  
Gradient Descent ◽  
Likelihood Function ◽  
Error Function ◽  
Complex Problem ◽  
Descent Method ◽  
Gold Price ◽  
Price Forecasting ◽  
Gradient Descent Method ◽  
Forecasting Accuracy ◽  
Median Error

Forecast of prices of financial assets including gold is of considerable importance for planning the economy. For centuries, people have been holding gold for many important reasons such as smoothening inflation fluctuations, protection from an economic crisis, sound investment etc.. Forecasting of gold prices is therefore an ever important exercise undertaken both by individuals and groups. Various local, global, political, psychological and economic factors make such a forecast a complex problem. Data analysts have been increasingly applying Artificial Intelligence (AI) techniques to make such forecasts. In the present work an inter comparison of gold price forecasting in Indian market is first done by employing a few classical Artificial Neural Network (ANN) techniques, namely Gradient Descent Method (GDM), Resilient Backpropagation method (RP), Scaled Conjugate Gradient method (SCG), Levenberg-Marquardt method (LM), Bayesian Regularization method (BR), One Step Secant method (OSS) and BFGS Quasi Newton method (BFG). Improvement in forecasting accuracy is achieved by proposing and developing a few modified GDM algorithms that incorporate different optimization functions by replacing the standard quadratic error function of classical GDM. Various optimization functions investigated in the present work are Mean median error function (MMD), Cauchy error function (CCY), Minkowski error function (MKW), Log cosh error function (LCH) and Negative logarithmic likelihood function (NLG). Modified algorithms incorporating these optimization functions are referred to here by GDM_MMD, GDM_CCY, GDM_KWK, GDM_LCH and GDM_NLG respectively. Gold price forecasting is then done by employing these algorithms and the results are analysed. The results of our study suggest that  the forecasting efficiency improves considerably on applying the modified methods proposed by us.

Classification and Prediction with Neural Networks

2011 ◽  
pp. 76-107
Author(s):  
Arnošt Veselý
Keyword(s):  
Neural Networks ◽  
Error Function ◽  
Descent Method ◽  
Cross Entropy ◽  
Gradient Descent Method ◽  
Classification Problems ◽  
Network Training ◽  
The Neural Network ◽  
Gradient Calculation ◽  
Entropy Error

This chapter deals with applications of artificial neural networks in classification and regression problems. Based on theoretical analysis it demonstrates that in classification problems one should use cross-entropy error function rather than the usual sum-of-square error function. Using gradient descent method for finding the minimum of the cross entropy error function, leads to the well-known backpropagation of error scheme of gradient calculation if at the output layer of the neural network the neurons with logistic or softmax output functions are used. The author believes that understanding the underlying theory presented in this chapter will help researchers in medical informatics to choose more suitable network architectures for medical applications and that it helps them to carry out the network training more effectively.

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