Influence Maximization in Social Networks When Negative Opinions May Emerge and Propagate

TLDR

Influence maximization seeks a small set of seed nodes that maximizes influence spread under cascade models, as defined by Kempe, Kleinberg, and Tardos (2003). This work extends the independent cascade model to account for the emergence and propagation of negative opinions. The authors introduce a quality factor to capture product defect–induced negativity, incorporate negativity bias, prove submodularity enabling a 1–1/e greedy approximation, define a quality‑sensitivity ratio with tight bounds, and develop an efficient tree‑based algorithm that underpins a heuristic for general graphs. Simulations demonstrate that the heuristic achieves influence comparable to the standard greedy algorithm while being orders of magnitude faster.

Abstract

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 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 compute 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.