Relative influence maximization in competitive social networks

Dingda Yang, Xiangwen Liao, Huawei Shen, Xueqi Cheng, Guolong Chen
2017 Science China Information Sciences  
In many realistic scenarios, such as political election and viral marketing, two opposite opinions, i.e., positive opinion and negative opinion, spread simultaneously in the same social networks [1, 2] . Consequently, to achieve good word-of-mouth effect, it is desired to maximize the spread of positive opinions while reducing the spread of negative opinions, i.e., maximizing the difference between the spread of positive opinions and the spread of negative opinions. In this article, we study
more » ... relative influence maximization (RIM) problem, which seeks to select initial individuals as a positive seed set under the existence of negative individuals, maximizing the difference between the spread of positive opinions and the spread of negative opinions, i.e., the relative influence. Existing methods approximately solve this problem either by promoting the spread of positive influence [1] or by limiting the spread of negative influence [2] . In this article, we theoretically analyze the intrinsic complexity of this problem and empirically develop efficient method to directly solve the RIM problem in social networks. To describe the spread of two competitive opinions, we introduce a competitive independent cas-cade (CIC) model by extending the classical independent cascade (IC) model [3] . In CIC model, each individual is in one of three states, i.e., inactive, P-active and N-active. Individuals in inactive states are not influenced. Individuals in P(N)active states stand for those who adopt the positive (negative) opinions. The diffusion process of positive and negative opinions unfolds independently as in IC model. When an individual is influenced by both positive and negative opinions simultaneously, negative opinion dominates over positive opinion, following the empirical observations [1] . Given such a competitive diffusion model, a network G = (V, E), a set of initial adopters of negative opinions I N , and a positive integer k, RIM aims to select an optimal positive seed set I P with k nodes so that P-active individuals are more than N-active individuals as many as possible in the end of diffusion. Mathematically, the RIM problem could be formalized as I P = arg max |IP |=k,IP ⊆V \IN {σ P (I P |I N ) − σ N (I P |I N )}, where σ P (I P |I N ) and σ N (I P |I N ) are the spread of the positive and negative opinions, respectively.
doi:10.1007/s11432-016-9080-3 fatcat:otb5ire555cf5nwjgcxvpdoova