💥1 概述
在本文中,实现了一个径向基函数(RBF)神经网络,用于预测混沌时间序列预测。特别是设计了一种麦基格拉斯时间序列预测模型,该模型可以使用过去的时间样本预测前进几步的值。RBF 使用传统的梯度下降学习算法进行训练,核函数是从 K 均值聚类算法获得的中心和扩散的高斯核。
📚2 运行结果
部分代码:
%% Results % Input and output signals (training phase) figure plot(indt,f_train,'k','linewidth',lw); hold on; plot(indt,y_train,'.:b','linewidth',lw); xlim([start_of_series_tr+time_steps end_of_series_tr]); h=legend('Actual Value (Training)','RBF Predicted (Training)','Location','Best'); grid minor xlabel('Sample #','FontSize',fsize); ylabel('Magnitude','FontSize',fsize); set(h,'FontSize',12) set(gca,'FontSize',13) saveas(gcf,strcat('Time_SeriesTraining.png'),'png') % Input and output signals (test phase) figure plot(indts,f_test,'k','linewidth',lw); hold on; plot(indts,y_test,'.:b','linewidth',lw); xlim([start_of_series_ts+time_steps end_of_series_ts]); h=legend('Actual Value (Testing)','RBF Predicted (Testing)','Location','Best'); grid minor xlabel('Sample #','FontSize',fsize); ylabel('Magnitude','FontSize',fsize); set(h,'FontSize',12) set(gca,'FontSize',13) saveas(gcf,strcat('Time_SeriesTesting.png'),'png') % Objective function (MSE) (training phase) figure plot(start_of_series_tr:end_of_series_tr-1,10*log10(I(1:end_of_series_tr-start_of_series_tr)),'+-b','linewidth',lw) h=legend('RBF (Training)','Location','North'); grid minor xlabel('Sample #','FontSize',fsize); ylabel('MSE (dB)','FontSize',fsize); set(h,'FontSize',12) set(gca,'FontSize',13) saveas(gcf,strcat('Time_SeriesTrainingMSE.png'),'png') % Objective function (MSE) (test phase) figure plot(start_of_series_ts+time_steps:end_of_series_ts,10*log10(I(end_of_series_tr-start_of_series_tr+1:end)),'.:b','linewidth',lw+1) h=legend('RBF (Testing)','Location','South'); grid minor xlabel('Sample #','FontSize',fsize); ylabel('MSE (dB)','FontSize',fsize); set(h,'FontSize',12) set(gca,'FontSize',13) saveas(gcf,strcat('Time_SeriesTestingMSE.png'),'png') % Mean square error 10*log10(((f_train'-y_train)*(f_train'-y_train)')/length(y_train)) 10*log10(((f_test'-y_test)*(f_test'-y_test)')/length(y_test))
🎉3 参考文献
[1]Shujaat Khan (2022). Mackey Glass Time Series Prediction using Radial Basis Function (RBF) Neural Network.
🌈4 Matlab代码实现
回复:基于径向基函数 (RBF) 神经网络的麦基格拉斯时间序列预测