Abstract: Influence maximization is to seek a group of most influential users in social networks as seed nodes,and spread information through seed nodes to maximize the information spreading.Most of the existing research on influence maximization assume that each node is either a seed or not.While in practical applications,the users’ probability of becoming a seed should be determined according to their influence in the social network,hence maximize the expected range of influence of the seed set obtained according to the probability distribution.This is the problem of continuous influence maximization.A continuous influence maximization algorithm under the independent cascade propagation model is proposed.The algorithm first abstracts the problem into a constrained optimization,then several possible seed sets are sampled.The influence propagation range is estimated for each possible seed set.The gradient descent method is employed to calculate the increment value in each direction according to the estimated propagation range in each iteration.The direction of the maximum increment is taken as the gradient to update the objective function value.By such iterations,the optimal solution of the objective function can be obtained.Experiments on real and virtual data sets show that the proposed algorithm can obtain significantly larger expected range of influence than Random,Degree,UD and CD algorithms.

Key words: Continuous influence maximization, Social networks, Independent cascade propagation model, Gradient descent, Iteration