Ceiling effect of online user interests for the movies

Online users' collective interests play an important role for analyzing the online social networks and personalized recommendations. In this paper, we introduce the information entropy to measure the diversity of the user interests. We empirically analyze the information entropy of the objects selected by the users with the same degree in both the MovieLens and Netflix datasets. The results show that as the user degree increases, the entropy increases from the lowest value at first to the highest value and then begins to fall, which indicates that the interests of the small-degree and large-degree users are more centralized, while the interests of normal users are more diverse. Furthermore, a null model is proposed to compare with the empirical results. In a null model, we keep the number of users and objects as well as the user degrees unchangeable, but the selection behaviors are totally random in both datasets. Results show that the diversity of the majority of users in the real datasets is higher than that the random case, with the exception of the diversity of only a fraction of small-degree users. That may because new users just like popular objects, while with the increase of the user experiences, they quickly become users of broad interests. Therefore, small-degree users' interests are much easier to predict than the other users', which may shed some light for the cold-start problem.