Dimension Reduction of Collective Attention Networks

Abstract

Recently, the dynamics of the collective attention of various cultural products are typically modeled by mathematical models. In this article, we propose a simple collective attention model for capturing the dynamics of coupled cultural products, which is represented by a complex dynamical network. In particular, the coupling mechanism of the model involves one of the cooperative, exploitative competitive, and appropriative terms. To facilitate the analysis of the higher-dimensional complex dynamical network, we employ and extend the existing dynamical dimension reduction techniques to reduce the network to a simplified lower-dimensional version. It can then be used to describe the collective dynamics of the original system, such as the emergency of the bifurcation of the collective attention received by cultural products. We test the dimension reduction techniques on several collective attention dynamical networks. Our results indicate that articulating the complex dynamical models as well as their advanced theories and tools may open up a new avenue for the dynamics study of collective attention.