Maximizing positive influence in competitive social networks: A trust-based solution
Introduction
Social influence is a crucial component of social network analysis used in a wide range of applications, including resource recommendation [4], [9], [18], viral marketing [16], [21], [25], and community detection [3], [10]. The subject of influence analysis consists of a set of problems that are central to the disciplines of computer science and sociology. In this field, the critical problem is to search a set of initial spreaders (seeds) for which receives the first-level of information and leads to an extensive range of influence spread. This problem is NP-hard, which is known as influence maximization (IM) [14].
The range of relationship-based information diffusion reflects a user’s influence ability. Almost all related work conventionally uses information cascade technology to model the processes of influence spread on real-world networks [4]. In the simple example of influence diffusion model (Fig. 1), users at the bottom of a diffusion chain are influenced by directly linked users (blue circles). Meanwhile, these users at the bottom are possible to be influenced by indirectly linked users according to the information diffusion theory [6]. However, there may be no information cascade between indirectly linked users (red dotted lines). Since the lack of directly measurable data, it is difficult to accurately simulate the diffusion [17]. In this example, it is easy to model the influence that spreads from user C to D. Then, users A and B are possible to influence user D, but it is hard to simulate the influence diffusion.
Similar to the above example, the previously related methods cannot truly portray the processes of influence spread and thus lead to the errors of estimating influence probabilities. Moreover, the IM problem becomes more challenging since two or more competitive items exist in online social networks (OSNs), which but frequently happened in real life [5]. As an essential concept in social network analysis, evidence shows that trust is among the most important factors for users’ decision-makings [6]. Trust is a measure of confidence that an entity or entities will behave expectedly [2]. A trusted user could potentially lead users to accept his/her opinions and make informed decisions. Trust and distrust relationships play different roles in accepting and rejecting a user’s influence. Interest in the models of competitive influence diffusion involves trust relationships has been increasing over the past few years, and it is now an essential issue in influence maximization.
Extensive studies have explored the method of detecting seed sets [1], [5], [6], [8], [15], [16], [25], [31], [32], there are two typical approaches to maximizing competitive influence (detecting positive or negative seeds). While researchers generally concur that two opposite type of seeds are used in the spread of competitive influence, there is agreement in the literature that the CIM problem can be solved by detecting positive seeds [1], [16], [17], [19], [31]. However, the effect of trust in the spread of competitive influence has not yet been systematically investigated. Meanwhile, conventional methods typically block opponents’ influence in the spread of competitive influence. Preventing opponents’ influence seems to make no sense because it is in an unrealistic situation and takes high computational time [1]. Thus, it is essential to develop an effective method of maximizing positive influence, and this study focused on detecting positive seeds for the CIM problem. In addition, several recent works consider trust relationships in their IM algorithms, but these methods assume trust values are given directly [6], [30]. This simple assumption may result in inaccurate trust values and thus leads to the poor performance of detecting seeds. This study has primarily concerned with competitive influence modeling based on trust evaluation and the efficiency problem of seed detection.
In this study, we devised a new trust-based solution that addresses the above challenges, which maximizes positive influence on OSNs under competing cascades. This solution highlights the effect of trust relationships in the spread of competitive influence. First, we established a new model of trust-based competitive influence diffusion (TrCID) that simulates the dynamic spreads of competitive influence. Trust relationships are used to model positive influence, and distrust relationships are used to model negative influence. Next, we estimated trust values through generalized network flows and used these results to calculate positive influence probabilities in TrCID. Finally, we developed an algorithm of trust-based competitive influence maximization (TrCIM) that efficiently calculates the positive marginal gain for non-seed users. To our knowledge, this may be the first work on maximizing positive influence in competitive social networks based on trust evaluations. This study conducted various comparisons on synthetic and real-world datasets, and the experimental results illustrate that our method performs better than other baselines. The main contributions of this study are summarized as follows.
- •
This work established the TrCID model that simulates the dynamic spreads of competitive influence, which incorporates the factors of trust and time decay. Our method estimates influence probabilities between users based on trust evaluations.
- •
This work developed the TrCIM algorithm that iteratively detects the seeds with the largest positive marginal gains. Meanwhile, this algorithm maintains good performance of spreading positive influence on OSNs.
- •
This work conducted extensive comparisons on different datasets. The experimental results illustrate the effectiveness and efficiency of our approach, and it is more practical than other baselines on real-world social networks.
The plan of this paper is as follows. Section 2 presents related works. Section 3 defines the problem of maximizing competitive influence and presents a solution framework. Then, Sections 4 Competitive influence diffusion model, 5 Estimating influence probability, 6 Discovering seed set introduce the TrCID model, the method of estimating influence probabilities, and the TrCIM algorithm, respectively. Next, Section 7 provides the evaluation of our approach and other baselines. Finally, Section 8 presents some concluding remarks and future directions.
Section snippets
Related work
In this section, we briefly review the related works that best line up with our solution, including influence diffusion models and influence maximization algorithms.
Solution overview
In this section, we define the problem of maximizing competitive influence and present a solution framework for this problem. The primary notations and corresponding descriptions are summarized in Table 1.
Competitive influence diffusion model
This section presents the details of the TrCID model (Algorithm 1), which considers both positive activations (using trust relationships) and negative activations (using distrust relationships). Extending the linear threshold model (LT) [4], [27], we reconsider the property of competitiveness based on positive and negative influence. The properties of dynamic diffusion and the rules of influence spread are also critical to model the spread of competitive influence.Algorithm 1. TrCID model Input:
Estimating influence probability
This section presents a method of estimating influence probabilities based on trust evaluations. Inspired by the effect of generalized network flows in trust evaluations [12], a modified method of generalizing flows is devised to estimate trust values between users, including trust decay modeling, generalized flow network construction, and generalized flow calculation. Then, this method uses the values of trust and distrust to estimate positive () and negative influence probabilities (
Greedy algorithm
Given a social network , we develop a new algorithm of detecting positive seeds, which is based on the TrCID model and the results of trust evaluation. Although the CIM problem is computationally complex, the influence function under the TrCID model satisfies the properties of monotonicity and submodularity, which are formally described as follows. Property 1 An influence function is monotone iff for any . Property 2 An influence function is submodular iff
Evaluation
This study compared the performance of the TrCIM algorithm with that of four baselines on synthetic and real-world datasets. We retrieved seeds returned by different algorithms to verify the effectiveness of TrCIM. We used different algorithms to detect seed users under the same condition of the influence probabilities calculated via the TrCID model. Then, we compared the spread of positive influence initiated by the seed users under the CLT model [4]. Finally, we employed an average spread for
Conclusion
This study offers a fresh perspective on how to devise the approach of maximizing competitive influence. Different from conventional approaches, this study developed a trust-based solution that maximizes competitive influence on OSNs. The newly established TrCID model emphasizes the effect of trust relationships in the spread of competitive influence and provides a solid foundation for solving the CIM problem. Then, this work developed the TrCIM algorithm via pruning the MC simulations, which
CRediT authorship contribution statement
Feng Wang: Conceptualization, Methodology, Software, Writing - original draft. Jinhua She: Data curation, Writing - review & editing. Yasuhiro Ohyama: Visualization, Supervision. Wenjun Jiang: Investigation, Validation. Geyong Min: Writing - review & editing. Guojun Wang: Supervision. Min Wu: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported by China Postdoctoral Science Foundation under Grant 2019M662740, the National Natural Science Foundation of China under Grant 61733016, 61632009 and 61502161, the 111 Project of China under Grant B17040, the Fundamental Research Funds for the Central Universities under Grant CUGCJ1812, the Guangdong Provincial Natural Science Foundation of China under Grant No. 2017A030308006, and the High Level Talents Program of Higher Education in Guangdong Province under Funding
References (32)
- et al.
A trust model for analysis of trust, influence and their relationship in social network communities
Telematics and Informatics
(2019) - et al.
A new algorithm for positive influence maximization in signed networks
Information Sciences
(2020) - et al.
Analyzing competitive influence maximization problems with partial information: an approximation algorithmic framework
Performance Evaluation
(2015) - et al.
Containment of competitive influence spread in social networks
Knowledge-Based Systems
(2016) - et al.
Maximizing positive influence spread in online social networks via fluid dynamics
Future Generation Computer Systems
(2018) - et al.
Influence maximization by leveraging the crowdsensing data in information diffusion network
Journal of Network and Computer Applications
(2019) - et al.
Identification of influential users in social networks based on users’ interest
Information Sciences
(2019) - et al.
A most influential node group discovery method for influence maximization in social networks: a trust-based perspective
Data and Knowledge Engineering
(2019) - N. Arazkhani, M.R. Meybodi, A. Rezvanian, Influence blocking maximization in social network using centrality measures,...
- et al.
Fast detection of community structures using graph traversal in social networks
Knowledge and Information Systems
(2019)
Positive opinion influential node set selection for social networks: considering both positive and negative relationships
Wireless Communications, Networking and Applications
Maximizing the spread of positive influence in signed social networks
Intelligent Data Analysis
Personalized review recommendation based on users’ aspect sentiment
ACM Transactions on Internet Technology
Cited by (36)
Attention-based neural networks for trust evaluation in online social networks
2023, Information SciencesAn improved competitive particle swarm optimization algorithm based on de-heterogeneous information
2023, Journal of King Saud University - Computer and Information SciencesMAHE-IM: Multiple Aggregation of Heterogeneous Relation Embedding for Influence Maximization on Heterogeneous Information Network
2022, Expert Systems with ApplicationsIdentifying influential nodes in social networks: Centripetal centrality and seed exclusion approach
2022, Chaos, Solitons and FractalsCitation Excerpt :Theoretical and applied research on complex networks in online information propagation has received extensive interest [1-3].
Opinion influence maximization problem in online social networks based on group polarization effect
2022, Information Sciences