Evolving Influence Maximization in Evolving Networks

Abstract

Influence Maximization (IM) aims to maximize the number of people that become aware of a product by finding the “best” set of “seed” users to initiate the product advertisement. Unlike most prior arts on the static networks containing fixed number of users, we study the evolving IM in more realistic evolving networks with temporally growing topology. The task of evolving IM, however, is far more challenging over static cases in the sense that the seed selection should consider its impact on future users who will join network during influence diffusion and the probabilities that users influence one another also evolve over time. We address the challenges brought by network evolution through EIM, a newly proposed bandit-based framework that alternates between seed nodes selection and knowledge (i.e., nodes’ growing speed and evolving activation probabilities) learning during network evolution. Remarkably, the EIM framework involves three novel components to handle the uncertainties brought by evolution: (1) A fully adaptive particle learning of nodes’ growing speed for accurately estimating future influenced size, with real growing behaviors delineated by a set of weighted particles. (2) A bandit-based refining method with growing arms to cope with the evolving activation probabilities via growing edges from previous influence diffusion feedbacks. (3) Evo-IMM , an evolving seed selection algorithm, which leverages the Influence Maximization via Martingale (IMM) framework, with the objective to maximize the influence spread to highly attractive users during evolution. Theoretically, the EIM framework returns a regret bound that provably maintains its sublinearity with respect to the growing network size. Empirically, the effectiveness of the EIM framework is also validated with three notable million-scale evolving network datasets possessing complete social relationships and nodes’ joining time. The results confirm the superiority of the EIM framework in terms of an up to 50% larger influenced size over four static baselines.