Nonlinear dynamics model for social popularity prediction based on multivariate chaotic time series

In online social network, it is of great significance in the popularity perception of social topics. Aiming to deeply analyze the nonlinear dynamics mechanism in the propagation process of social topics, the chaotic characteristics of information dissemination are thoroughly explored in this paper, and Bayesian estimation theory is employed to integrate the cross-platform factors affecting the topic popularity. Firstly, the time series of topic popularity from different platforms are redefined. And Principal Component Analysis (PCA) method is introduced to quantize the redefined time series and receive the main components affecting popularity. Secondly, this paper focuses on specific topics and performs small-data method to calculate the maximum Lyapunov exponent, which can be found that there are chaotic characteristics in time series of topic popularity. Then, the main components affecting popularity are reconstructed based on the phase space reconstruction theory, and the chaotic attractor is recovered in the high-dimensional reconstructed phase space. Smoothly, the evolution regularities and properties of complex system are restored to perceive the propagating situation of topic popularity. At the same time, the novel and fused phase space is obtained by using the Bayesian estimation theory to optimally fuse multiple variables in the same high-dimensional space. Finally, RBF (Radial Basis Function) neural network is employed to predict the fused popularity due to its strong ability to approximate nonlinear functions. Experiments show that the prediction approach can not only merge topic popularity from multiple social platforms, but also can improve the prediction accuracy to some degree. In the meanwhile, the developing trend of topics can be perceived from a more fine-grained perspective.