Abstract
Shallow models have limited ability to express high-dimensional nonlinear complex functions. Based on deep learning, a Gaussian radial basis function neural network (RBFNN) is proposed, which is an analysis method of nonlinear complex function approximation based on the Gaussian-RBFNN model. The proposed method can approximate single-variable and binary complex nonlinear functions, and the approximation error is less than 0.1, which can achieve the ideal approximation effect. Finally, the proposed method is applied to analyze the nonlinear complex stock prediction approximation problem, and the effectiveness and practicality of the method are further verified. It can be seen that compared with the BP neural network model, this model performs better in average training time, training standard error, Ratt, RATR, and trmse For RBFNN; the training only needs 50 iterations, while the traditional BP needs 7100 training to gradually converge. In the actual function test, after 275 times of training, the convergence speed gradually tends to be stable, and the predicted value is closer to the actual value. Therefore, the model can be used to analyze practical nonlinear complex function approximation problems.
Highlights
Compared with the deep learning model, the improved shallow model still has some limitations in processing and analyzing nonlinear complex problems. erefore, based on the radial basis function neural network (RBFNN) model, with Gaussian as kernel function, a Gaussian-RBFNN nonlinear complex function approximation method is proposed
Compared with the BP neural network model, the proposed model has significantly better approximation ability to the nontraining samples, almost complete approximation
Compared with the comparison model, the predicted value of the proposed model is closer to the actual value, and the fitting effect of the predicted value curve and the actual value curve is better. us, the proposed model has higher prediction accuracy and better prediction effect
Summary
With the development of intelligent technology and other high and new technologies, product functions gradually tend to be complex, resulting in the response time and parameters of the corresponding functions of products showing nonlinear and complex many-to-many characteristics. Based on the BP neural network model and the network model with support vector machine (SVM), etc., there are only computing nodes of the hidden layer It can express the nonlinear simple mapping relationship, which can achieve ideal expression effect. When the training sample is small, the expression ability of the model has certain limitations [1, 2] To solve this problem, some scholars try to improve the traditional shallow mathematical model to improve the approximation and expression of high-dimensional nonlinear complex functions. Applied the nonlinear function to GDP prediction and achieved good results, which laid the foundation for this study [9–13] It provides a reference for the application of the traditional shallow mathematical model for the analysis of complex nonlinear problems. Compared with the deep learning model, the improved shallow model still has some limitations in processing and analyzing nonlinear complex problems. erefore, based on the RBFNN model, with Gaussian as kernel function, a Gaussian-RBFNN nonlinear complex function approximation method is proposed
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