Computation of Activation Probabilities in the Independent Cascade Model

Abstract

Based on the concepts of word-of-mouth effect and viral marketing, the diffusion of an innovation may be triggered starting from a set of initial users. Estimating the influence spread is a preliminary step to determine a suitable or even optimal set of initial users to reach a given goal. In this paper, we focus on a stochastic model called the Independent Cascade model, and compare a few approaches to compute activation probabilities of nodes in a social network, i.e., the probability that a user adopts the innovation. In the paper, first we propose the Path Method which computes the exact value of the activation probabilities but it has high complexity. Second an approximated method, called SSS-Noself, is obtained by modification of the existing SteadyStateSpread algorithm, based on fixed-point computation, to achieve a better accuracy. Finally an efficient approach, also based on fixed-point computation, is proposed to compute the probability that a node is activated though a path of minimal length from the seed set. This algorithm, called SSS-Bound-t algorithm, can provide a lowerbound for the computation of activation probabilities.

On Fast and Effective Influence Spread Maximization in Social Networks

“…In [25] the authors propose the Path Method, an algorithm to exactly compute the value of π j (φ 0 ) for IC networks. This algorithm takes into account all the possible evolutions of the information spread in a social network.…”

“…Due to the high complexity of the Path Method, its computational time is O(6 N ) [25]. The exponential complexity of this approach makes it not feasible for large-scale networks.…”

“…• For the sake of exactly computing the influence spread in a social network based on the LT diffusion model, we extend to the LC case the Path Method proposed by [25] for the IC diffusion model only. • Leveraging on the SteadyStateSpread approach proposed by [15] to iteratively calculate the influence spread in IC networks, we present its counterpart for LT models, proving its convergence to a fixed point.…”

A method for determining information diffusion cascades on social networks

“…A lot of existing studies adopt the Linear Threshold model (LT model) [4][5][6][7] and Independent Cascade model (IC model) [8][9][10] to predict diffusion cascades. In the former, an acceptance threshold θ and an aggregation function f are associated with each user (or node).…”

Influence Maximization in Independent Cascade Networks Based on Activation Probability Computation

“…In order to improve the accuracy of activation probability computation, in our previous paper [23], we proposed a new SSS-Noself algorithm for the influence spread evaluation under the Independent Cascade model. Experimental results show that our SSS-Noself algorithm performs well in terms of value approximation.…”