Influence Maximization in Social Networks When Negative Opinions May Emerge

Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 − 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of Θ( √ n/k) on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to com∗Author affiliations and emails: W. Chen (contact author), Microsoft Research Asia, China, [email protected]. A. Collins, Google Inc., U.S.A., [email protected]. R. Cummings, University of Southern California, U.S.A., [email protected]. T. Ke, University of California at Berkeley, U.S.A., [email protected]. Z. Liu, Harvard University, U.S.A., [email protected]. D. Rincon, Universitat Politècnica de Catalunya, Spain, [email protected]. X. Sun, Shanghai Jiao Tong University, China, [email protected]. Y. Wang, Microsoft Research Asia, China, [email protected]. W. Wei, Carnegie Mellon University, U.S.A., [email protected]. Y. Yuan, University of Pennsylvania, U.S.A., [email protected]. The work was done when all authors were working at or visiting Microsoft Research Asia. †An extended abstract appears in Proceedings of SIAM International Conference on Data Mining (SDM), 2011. This is the 2nd revision, which includes a minor fix to the pseudocode in Algorithm 3. pute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster. keywords: influence maximization; social networks; negative opinions; independent cascade model;