Identification of Top-K Influencers Based on Upper Confidence Bound and Local Structure

Abstract

We study the problem of identifying top-K influencers when we have only local knowledge of the network structure. More specifically, the selection of top-K influencers is performed sequentially over a number of rounds. We propose an efficient algorithm called strength network similarity-based upper confidence bound (SNS_UCB1) for the identification of top-K influencers based on upper confidence bound (UCB1) from the multi-armed bandit's framework. Considering feedback in online decision-making, we rely on edge (arm) strength on falling within a large number of other edges and how edge members are similar to each other and can thus convince other users to adopt the promoted behaviours. Thus, this feedback is considered as a reward score at each pull of the arm of how likely this selection is to contribute to the increase in the cumulative reward. We evaluate the proposed algorithm under the independent cascade (IC) model on four large-scale datasets that differ in size and density. We compare our algorithm to a centrality measure-based UCB1 and several well-known state-of-the-art approaches, demonstrating its superior performance in terms of influence spread achieved with the less required time and storage space.

Introduction

Online social networks or social media are widely used by billions around the globe and present a ubiquitous lifestyle routine. The wide spread of various social media platforms that let people get in touch, share data and interact easily online for various purposes is unprecedented. Influence maximization is one of interesting research topics that has attracted the attention of the research community from various fields and disciplines. It has been found to have potential applications in viral marketing that aims to influence a small number of nodes called the main seed set that will result in a large cascading process. Specifically, the influence maximization problem attempts to intelligibly identify the top-K influencers that will affect a large number of users within the network after having been selected to promote ideas, content, products, and innovations. Numerous studies have addressed this problem, and Kempe et al. [1] were the first to address this problem as a combinatorial problem and prove that the problem of identification of top-K influencers was NP-hard. The researchers proposed a greedy hill climbing algorithm that was observed to outperform others in terms of achieving a higher influence spread, while suffering from noticeable scalability issues; as argued by Chen et al. [2], running the greedy algorithm with a few hundred thousand nodes involved a high time complexity for completing the identification of the seed set on a modern server. While various efforts have been made to optimize the running time [3][4][5], this factor remains the main drawback of approaches based on a greedy algorithm applied to a moderately large graph. Other studies have tried to propose methods based on centrality measures that provide performance guarantees regarding the spread of influence with a low running time [2][6][7][8][9]. Other approaches have tried to learn the propagation probability of a diffusion model as the main ingredient for increasing the number of influenced users but did not take into account any diffusion models; those studies include methods based on algorithms called “multi-armed bandits”. Similarly, the use of structural network properties has led to some performance improvements in the influence coverage and low runtime complexity in various research studies. Hence, the selection of top-K influencer-based network measures seems promising when exploiting centrality measures and trying to boost the spread of influence in online decision-making in which the marketer may decide at each round to choose (or not) a candidate user as a seed set, aiming to increase the cumulative reward and equivalently minimize the regret. The multi-armed bandits' algorithms have been used recently in influence maximization, and their performance in learning the propagation probability and thus reducing regret has been demonstrated [10][11][12].

The aspect of identification being a key constraint and an essential ingredient of the influence maximization problem leads to designing an effective strategy that requires a low running time and provides a higher influence spread. In this work, we consider the use of the upper confidence bound (UCB1) and its impact on the cascading process under the IC model. Unlike existing studies that focused on learning the propagation probability without any knowledge of the used diffusion models, the present work deals with the identification of top-K influencers by using a UCB1 algorithm-based newly designed local measure that aggregates the strength of edges (arms) and the similarity of edge members to each other. This newly designed measure is used as a reward to efficiently select arms¹ and edges to locate the edge that is attached to the highest number of other edges locally up to a certain number of hops. Thereafter, the reward is fed into the UCB1 algorithm from the MAB framework, and the arms are sequentially selected according to reward score value, which depends mainly on local centrality measures that significantly reduce the running time of the designed algorithm. After the selection of arms, the candidate seed set is selected according to their degree. Hence, our approach is independent of the used diffusion models and tries to select the most influential users based only on structural properties and on the number of times the arms are selected; the more times an arm has been selected, the less likely it is to be chosen.

The purpose of this paper is to prominently select the best top-K influencers based only on the local structure using an online learning algorithm called upper confidence bound (UCB1), which guarantees a low time and storage space complexity, while providing an acceptable influence spread. The main contributions of this work can be outlined as follows:

• Proposing a new reward function that locally measures the arm strength and arm member similarity;

• Introducing a new algorithm called the strength network similarity-based upper confidence bound (SNS_UCB1);

• Evaluating the proposed algorithm with four real-world datasets under the independent cascade (IC) model;

• Comparing the proposed algorithm to state-of-the-art approaches in terms of time complexity, storage needed and influence achieved under the IC model; and

• Comparing the proposed SNS_UCB1 algorithm to several centrality measures embedded in the UCB1 algorithm to test how our algorithm and the proposed measure perform in terms of influence achieved, required time, storage space, cumulative reward, and regret.

The rest of this paper is organized as follows. Section 2 discusses several studies most closely related to the proposed algorithm. Section 3 provides a formulation of the system model and introduces the proposed measure. Section 4 presents the SNS_UCB1 algorithm and its analysis and discusses the time and space complexity. The results of extensive experiments performed with the proposed algorithm are depicted in Section 5, followed by conclusions and a discussion of future research directions in Section 6.