Popularity and user diversity of online objects

The popularity has been widely used to describe the object property of online user-object bipartite networks regardless of the user characteristics. In this paper, we introduce a measurement namely user diversity to measure diversity of users who select or rate one type of objects by using the information entropy. We empirically calculate the user diversity of objects with specific degree for both MovieLens and Diggs data sets. The results indicate that more types of users select normal-degree objects than those who select large-degree and small-degree objects. Furthermore, small-degree objects are usually selected by large-degree users while large-degree objects are usually selected by small-degree users. Moreover, we define 15% objects of smallest degrees as unpopular objects and 10% ones of largest degrees as popular objects. The timestamp is introduced to help further analyze the evolution of user diversity of popular objects and unpopular objects. The dynamic analysis shows that as objects become popular gradually, they are more likely accepted by small-degree users but lose attention among the large-degree users.