Opinion Diversity Maximization in Social Networks

In recent years, the social networks play an important role as the information sources for many people. The algorithms applied by these platforms feed the users with opinions that meet their tastes. These algorithms, on the other hand, harm the free flow of information by forming filter bubbles and echo chambers. The motivation of the thesis is to break filter bubbles by maximizing the diversity of opinion exposures in a social network. To achieve the goal, we assume that we can change a limited number of users’ exposures to the information in the network. We propose two concrete models, bounded-box diversity maximization and the l2-bounded diversity maximization respectively. Both of them are convex maximization problems subject to different constraints. Besides the common cardinality constraint and linear constraint, the second model has an l2 constraint. We give a detailed exposition of convex maximization problems under different constraints. We prove that first problem can be discretized and transformed into the Quadratic Knapsack Problem (QKP), while the second one can not. Guided by convexity and QKP, Greedy Algorithms and Semidefinite Relaxation are applied. In a high level, the core idea of the Semidefinite Relaxation consist of two components: first, relaxing the original problem into Semidefinite Programming and obtaining a solution; second, rounding the solution to a feasible solution of the original problem through sampling from a Gaussian distribution. To evaluate our problem, we implement the algorithms on datasets that have clear chambers and low diversity structure. We show that semidefinite relaxation based algorithms work well when there are large changes on the cardinality, while when the changes are small, the greedy algorithms are comparable. The greedy algorithms have descent scalability for large datasets.