Small and multi-peak nonlinear time series forecasting using a hybrid back propagation neural network

Gushes of online public opinions may trigger unexpected incidents that significantly affect social security and stability. Number of posts published per time interval, which is a time series dataset featured with multiple small-scale peaks and nonlinearities, is a simple and direct indicator of how severe the situation is and how much attention has been attracted. Thus, it is of great interest and significance to be able to accurately forecast this type of time series datasets. In this paper, a hybrid Back Propagation Neural network (BPNN) model is proposed to predict the features of this kind of time series datasets. Specifically, a modified Particle Swarm Optimization (PSO) algorithm combined with an Information Entropy (IE) function is used to optimize the weights and thresholds of the network, and the Bayesian Regularization is applied during the training process. Two real online public opinion cases are investigated to verify the effectiveness of the proposed model. Results showed that the proposed model has better performance in accuracy and stability, compared with Levenberg-Marquardt (LM) based BPNN, PSO based BPNN, Bayesian Regularization (BR) based BPNN, Stochastic Gradient Descent (SGD) based BPNN and Least Squares Support Vector Machines (LS-SVM) models.