Unifying information propagation models on networks and influence maximisation

Abstract

Information diffusion in social networks is a central theme in computational social sciences, with important theoretical and practical implications, such as the influence maximisation problem for viral marketing. Two widely adopted diffusion models are the independent cascade model where nodes adopt their behaviour from each neighbour independently, and the linear threshold model where collective effort from the whole neighbourhood is needed to influence a node. However, both models suffer from certain drawbacks, including a binary state space, where nodes are either active or not, and the absence of feedback, as nodes can not be influenced after having been activated. To address these issues, we consider a model with continuous variables that has the additional advantage of unifying the two classic models, as the extended independent cascade model and the extended linear threshold model are recovered by setting appropriate parameters. For the associated influence maximisation problem, the objective function is no longer submodular, a feature that most approximation algorithms are based on but is arguably strict in practice. Hence, we develop a framework, where we formulate the influence maximisation problem as a mixed integer nonlinear programming and adopt derivative-free methods. Furthermore, we propose a customised direct search method specifically for the proposed diffusion model, with local convergence. We also show that the problem can be exactly solved in the case of linear dynamics by selecting nodes according to their Katz centrality. We demonstrate the rich behaviour of the newly proposed diffusion model and the close-to-optimal performance of the customised direct search numerically on both synthetic and real networks.