Influence Maximization Algorithm Research Articles

Budget-Aware Local Influence Iterative Algorithm for Efficient Influence Maximization in Social Networks

The budgeted influence maximization (BIM) problem aims to identify a set of seed nodes that adhere to predefined budget constraints within a specified network structure and cost model. However, it is difficult for the existing algorithms to achieve a balance between timeliness and effectiveness. To address this challenge, our study initially proposes a refined cost model through empirical scrutiny of Weibo's quote data. Subsequently, we introduce a proxy-based algorithm, i.e., the budget-aware local influence iterative (BLII) algorithm tailored for the BIM problem, aimed at expediently identifying seed nodes. The algorithm approximates the global influence by leveraging the user’s one-hop influence and circumvents influence overlap among seed nodes via iterative influence updates. Comparative experiments involving eight algorithms across four real networks demonstrate the effectiveness, efficiency, and robustness of the BLII algorithm. In terms of influence spread, the proposed algorithm outperforms other proxy-based algorithms by 20%–255% and reaches the state-of-the-art simulation-based approach by 96%. In addition, the running time of the BLII algorithm is reasonable. Generally, the proposed cost model and BLII algorithm provide novel insights and potent tools for studying BIM problems.

A General Concave Fairness Framework for Influence Maximization Based on Poverty Reward

Influence maximization (IM) aims to find a group of influential nodes as initial spreaders to maximize the influence spread over a network. Yet, traditional IM algorithms have not been designed with fairness in mind, resulting in discrimination against some groups, like LGBTQ communities and racial minorities, etc. This issue has spurred research on Fair Influence Maximization (FIM). However, existing FIM studies come with some drawbacks. Firstly, most proposed notions of fairness for FIM cannot adjust the trade-off between fairness level and influence spread. Secondly, though a few specific notions of fairness allow such balancing, they are limited to a few specific concave functions, which may not be suitable for various real-world scenarios. Furthermore, none of them have studied the deep relations between the features of concave functions and the level of fairness. Thirdly, existing fairness metrics are limited to their corresponding concepts of fairness. Comparing the level of fairness across different algorithms using existing metrics can be challenging. To tackle the above problems, this paper first proposes a novel fairness notion named Poverty Reward (PR), which achieves fairness by rewarding the enrichment of groups with low utility. Based on PR, we further propose an algorithmic framework called Concave Fairness Framework (CFF) that allows any concave function that satisfies specific requirements. We also systematically clarify how fairness is improved by applying concave functions and provide an in-depth quantitative analysis of how to select appropriate concave functions for different utility distributions. Moreover, we propose the Reward of Fairness (RoF) metric that evaluates the disparity between groups. Based on RoF, an evaluation system is built to uniformly compare FIM algorithms from different fairness notions. Experiments in real-world datasets have demonstrated the validity of the CFF, as well as the proposed fairness notion.

DiFuseR: a distributed sketch-based influence maximization algorithm for GPUs

DiFuseR: a distributed sketch-based influence maximization algorithm for GPUs

IMUNE: A novel evolutionary algorithm for influence maximization in UAV networks

In a network, influence maximization addresses identifying an optimal set of nodes to initiate influence propagation, thereby maximizing the influence spread. Current approaches for influence maximization encounter limitations in accuracy and efficiency. Furthermore, most existing methods are aimed at the IC (Independent Cascade) diffusion model, and few solutions concern dynamic networks. In this study, we focus on dynamic networks consisting of UAV (Unmanned Aerial Vehicle) clusters that perform coverage tasks and introduce IMUNE, an evolutionary algorithm for influence maximization in UAV networks. We first generate dynamic networks that simulate UAV coverage tasks and give the representation of dynamic networks. Novel fitness functions in the evolutionary algorithm are designed to estimate the influence ability of a set of seed nodes in a dynamic process. On this basis, an integrated fitness function is proposed to fit both the IC and SI (Susceptible–Infected) models. IMUNE can find seed nodes for maximizing influence spread in dynamic UAV networks with different diffusion models through the improvements in fitness functions and search strategies. Experimental results on UAV network datasets show the effectiveness and efficiency of the IMUNE algorithm in solving influence maximization problems.

The influence maximization algorithm for integrating attribute graph clustering and heterogeneous graph transformer

In social networks, maximizing influence is an important research direction. However, traditional influence maximization algorithms often overlook the attribute information of nodes and the heterogeneity of networks, leading to inefficiency and inaccuracy in the propagation process. To address this issue, this study first constructs a social network influence maximization propagation model, and then combines auto-encoder and graph convolutional autoencoder to extract social network user attributes. Finally, Transformer is used to learn the feature representation of social network nodes. Moreover, a heterogeneous graph neural network is introduced to combine with Transformer to further learn the feature representation of nodes, so as to design an influence maximization algorithm combining attributed graph clustering and heterogeneous graph Transformer. The results showed that the loss values of the fusion algorithm on different datasets were 0.619 and 0.17, respectively, proving its good fitting performance. The recall rate and F1 of this fusion algorithm were 92.5 % and 0.90, respectively, proving its high clustering accuracy. The influence maximization model based on fusion algorithm achieved active node coverage of 67 % and 48 % on two datasets, respectively, proving its good influence propagation effect. The above results demonstrate that the designed model can effectively spread influence. This helps to better understand and utilize the influence dissemination mechanisms in social networks, thereby promoting the development of social network research.

A Dominance Approach for Influence Maximization with Incomplete Information in Social Network

Influence maximization plays an important role in social network analysis and has been extensively explored due to its emergence in a great deal of applications. However, a vast majority of researchers have only considered the influence of one factor on the spread of information among individuals. In addition, this factor which is mainly the influence probability, has been considered to be fixed which is estimated based on the number of neighbors of each individual. While, in reality, we do not have complete information about this probability and it is not a fixed value. Moreover, in the spread of information, other factors including trust, are also involved, which cannot be easily combined due to their different nature. In this paper, a dominance approach to influence maximization is studied under the condition, in which, complete information about influence of users on each other is not available and users infect each other based on an unknown influence probability. Furthermore, in order to make the proposed model closer to reality, trust factor is also considered as an independent factor. The proposed method is compared to several state-of-the-art influence maximization algorithms and attained results on several synthetic and real social network datasets verify effectiveness of the proposed method compared to previous methods in the context of influence maximization.

Influence Maximization Based on Adaptive Graph Convolution Neural Network in Social Networks

The influence maximization problem is a hot issue in the research on social networks due to its wide application. The problem aims to find a small subset of influential nodes to maximize the influence spread. To tackle the challenge of striking a balance between efficiency and effectiveness in traditional influence maximization algorithms, deep learning-based influence maximization algorithms have been introduced and have achieved advancement. However, these algorithms still encounter two key problems: (1) Traditional deep learning models are not well-equipped to capture the latent topological information of networks with varying sizes and structures. (2) Many deep learning-based methods use the influence spread of individual nodes as labels to train a model, which can result in an overlap of influence among the seed nodes selected by the model. In this paper, we reframe the influence maximization problem as a regression task and introduce an innovative approach to influence maximization. The method adopts an adaptive graph convolution neural network which can explore the latent topology information of the network and can greatly improve the performance of the algorithm. In our approach, firstly, we integrate several network-level attributes and some centrality metrics into a vector as the presentation vector of nodes in the social network. Next, we propose a new label generation method to measure the influence of nodes by neighborhood discount strategy, which takes full account of the influence overlapping problem. Subsequently, labels and presentation vectors are fed into an adaptive graph convolution neural network model. Finally, we use the well-trained model to predict the importance of nodes and select top-K nodes as a seed set. Abundant experiments conducted on various real-world datasets have confirmed that the performance of our proposed algorithm surpasses that of several current state-of-the-art algorithms.

IMVis: Visual analytics for influence maximization algorithm evaluation in hypergraphs

Influence maximization (IM) algorithms play a significant role in hypergraph analysis tasks, such as epidemic control analysis, viral marketing, and social influence analysis, and various IM algorithms have been proposed. The main challenge lies in IM algorithm evaluation, due to the complexity and diversity of the spreading processes of different IM algorithms in different hypergraphs. Existing evaluation methods mainly leverage statistical metrics, such as influence spread, to quantify overall performance, but do not fully unravel spreading characteristics and patterns. In this paper, we propose an exploratory visual analytics system, IMVis, to assist users in exploring and evaluating IM algorithms at the overview, pattern, and node levels. A spreading pattern mining method is first proposed to characterize spreading processes and extract important spreading patterns to facilitate efficient analysis and comparison of IM algorithms. Novel visualization glyphs are designed to comprehensively reveal both temporal and structural features of IM algorithms’ spreading processes in hypergraphs at multiple levels. The effectiveness and usefulness of IMVis are demonstrated through two case studies and expert interviews.

Heterogeneous network influence maximization algorithm based on multi-scale propagation strength and repulsive force of propagation field

Heterogeneous networks, like social and academic networks are widespread in the real world, characterized by diverse nodes and complex relationships. Influence maximization is a crucial research topic, in these networks, as it can help in comprehending the mechanisms of information propagation and diffusion. Effectively utilizing complex structural information poses a challenge in current research on influence maximization in heterogeneous information networks. As a solution to this problem, a heterogeneous network influence maximization algorithm based on the multi-scale propagation strength and repulsive force of propagation field is proposed. Firstly, based on the propagation field, we design a multi-scale propagation strength index for the propagation ability of nodes to achieve maximum coverage of influence propagation. Specifically, in the homogeneous structure, the homogeneous propagation strength describes the propagation ability of nodes. In the heterogeneous structure, the heterogeneous shallow propagation strength and the heterogeneous deep propagation strength are designed to exploit the local and global spreading ability of nodes using meta-paths and link prediction based on graph neural networks, respectively. Secondly, to ensure the minimum overlap in the propagation range of seed nodes, we designed the overlapping repulsive force between node pairs in the propagation field. Finally, considering the complexity of the propagation process of heterogeneous information networks, an independent cascade model based on meta-paths is proposed. Based on experiments conducted with several datasets, our algorithm outperforms baseline algorithms for solving influence maximization problem.

A node-embedding-based influence maximization algorithm in temporal network

A node-embedding-based influence maximization algorithm in temporal network

PHEE: Identifying influential nodes in social networks with a phased evaluation-enhanced search

How to identify a small fraction of users with the best capacity to influence other users is central to the research of social network analysis. This problem is termed influence maximization (IM) and is known for its extensive applications. IM can be formulated as a combinatorial optimization problem, which has been shown to be NP-hard under some diffusion models. Therefore, seeking for high-accuracy IM algorithms with acceptable running time has attracted much attention in literature. However, most of existing IM algorithms only adopt a uniform mechanism in the whole solution search process, which lacks of flexible response when the algorithms trap in local optimum. This paper proposes a phased evaluation-enhanced (PHEE) approach for IM, which utilizes two distinct strategies to search the optimal solutions: The first one is a random range division-based evolutionary algorithm for improving solution quality; the second is a fast convergence strategy for searching an optimal solution. Two PHEE-based algorithms, MDD-PHEE and GCI-PHEE, are generated and are evaluated on 10 real-world social networks of different sizes and types. Experimental results demonstrate the effectiveness of PHEE; in particular, MDD-PHEE obtains the best influence spread on all networks compared with the state-of-the-art algorithms, and has a better performance than the time-consuming algorithm CELF on four datasets.

Network Dynamic GCN Influence Maximization Algorithm With Leader Fake Labeling Mechanism

Influence maximization is an important technique for its significant value on various social network applications, such as viral marketing, advertisement, and recommendation. Traditional heuristic algorithms for influence maximization suffer from different issues, such as accuracy descent and information loss during network exploration. Besides, recently proposed deep learning-based approaches cannot extract the in-depth structural information of social networks well. In light of these problems, we propose a novel heuristic method called the network dynamic GCN influence maximization algorithm based on the leader fake labeling mechanism. To exploit the in-depth network topology information for the influence maximization task, we design a network dynamic GCN that owns adaptive layer numbers in terms of different network scales to obtain node representations. Then, considering that there are few labels in the network or the labels are irrelevant to the task of influence maximization, we establish a leader fake labeling mechanism to automatically generate node labels that are helpful to seed nodes selecting for model training. Finally, a heuristic method based on the Mahalanobis distance is developed to quickly select influential seed nodes with the learned node representations. Three real-world datasets are used in our experiments, and the experimental results demonstrate that our algorithm has a better performance for seed set identification under the premise of high efficiency compared with some latest heuristic influence maximization algorithms.

Research on the Social Network Search Strategy from the Viewpoint of Comprehensive Influence Maximization

Considering that social network provides a channel for nodes to exchange information, resources, and interests, the fundamental task of social network search is to find the best path from the source node to the target node. The search strategy based on the shortest path principle ignores the strength and direction of the social relationship between nodes in the social network, and ignores the difference of influence between nodes, so that the search results cannot meet the needs of searchers. Considering the important role of the influence of nodes and the influence intensity between nodes in social network search, this paper proposes the path optimization principle of maximizing the comprehensive influence, and constructs a new search algorithm based on this strategy by applying the modified Dijkstra algorithm to solve the optimal path between nodes. Using the data of typical real social networks, it is verified that the path optimization algorithm based on the principle of maximizing comprehensive impact is better than the optimization algorithm based on the shortest path, and the search results are better interpretable to users. This paper had proposed a new influence maximization algorithm which has more advantages for solving social network search with high costs or benefits consideration by taking the influence intensity of nodes or between nodes into account.

Fast and error-adaptive influence maximization based on Count-Distinct sketches

Influence maximization (IM) is the problem of finding a seed vertex set that maximizes the expected number of vertices influenced under a given diffusion model. Due to the NP-Hardness of finding an optimal seed set, high-quality yet expensive approximation algorithms have been frequently used. In addition, lightweight, sketch-based approaches, which do not step-by-step simulate the influence process, have been proposed in the literature to cope with the scale of today's networks. In this work, we describe a fast, error-adaptive approach that leverages Count-Distinct sketches and hash-based fused sampling to avoid step-by-step simulations and estimate the number of influenced vertices throughout a diffusion. Furthermore, for faster estimations, the sketches of a vertex for consecutive simulations are stored adjacently in memory. This allows the proposed algorithm to estimate the number of influenced vertices for multiple simulations at once. For faster processing, the proposed method automatically rebuilds the sketches after observing estimation errors above a given threshold. Our experimental results show that the proposed algorithm yields seed sets with comparable quality while being up to 3,337× faster than a state-of-the-art, high-quality influence maximization algorithm. In addition, it is up to 63× faster than a sketch-based approach while producing seed sets with 2%–10% better influence scores.

Influence maximization algorithm based on group trust and local topology structure

Influence maximization is one of the important contents of social network analysis. Many classical influence propagation models assume that there is a stable information propagation phenomenon between adjacent users, and do not consider the influence of internal structure information of the network on the actual information propagation. Therefore, an influence maximization algorithm based on group trust and local topology structure is proposed. In order to make full use of the important role of group in information propagation, the concepts of intra-group connectivity, inter-group diffusion and group trust are defined based on the characteristics such as group tightness. Then, an influence propagation algorithm based on the local topological structure of the group is proposed to extract the local structure information of different topological positions in the group, and calculate the propagation probability between users. Finally, the seed nodes were selected according to the credibility ranking of the group for influence propagation. Experiments on multiple data sets show that compared with other algorithms, the algorithm can achieve higher propagation efficiency and wider influence effect, which verifies the rationality and effectiveness of the method.

A privacy‐sensitive data identification model in online social networks

AbstractPrivacy protection in online social networks (OSNs) has received a great deal of attention in recent years. One way of circumventing conventional privacy protection is privacy inference based on data that can be easily obtained in OSNs. Previous work on privacy inference has studied the issue mostly from the viewpoint of the attackers and methods thus designed were mostly aimed at pursuing the accuracy of the inference results with little regard on the causes of privacy breaches. To develop more effective privacy protection mechanisms that takes privacy inference into consideration, it is necessary to identify the information that plays a more important role in privacy breaches. In this paper, we propose a privacy‐sensitive data identification model in OSNs, which can identify key pieces of data that are most sensitive as far the privacy of the user is concerned. Firstly, a privacy inference method is proposed based on conditional random fields to infer the privacy of the target users. Then, a privacy‐sensitive data identification method is proposed by using the intermediate data of the proposed privacy inference method based on the targeted influence maximization algorithm. Thus, the key pieces of data in the form of user attributes and relationships on which the privacy of the target user depends can be determined to facilitate the implementation of privacy protection mechanisms. The effectiveness as well as the advantages of the proposed model is verified and demonstrated through experiment using real datasets. The impact of the key factors on privacy inference is also analyzed to guide the design of effective privacy protection strategies.

A Search Space Reduction-Based Progressive Evolutionary Algorithm for Influence Maximization in Social Networks

Influence maximization (IM) problem, which selects a subset of nodes from a social network to maximize the influence spread, appeals to numerous scholars. Since the IM problem is NP-hard, it is still an arduous task to achieve good results in terms of influence spread and running time at the same time. This article proposes a novel search space reduction strategy-based progressive evolutionary algorithm (SSR-PEA) for solving IM problems effectively and efficiently. In SSR-PEA, a novel search space reduction strategy (SSR) in the light of the power-law distribution of the social network is designed to reduce the computational overheads, which eliminates a great deal of less influential nodes in a sensible way. After that, we propose a progressive evolutionary framework based on SSR, where the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-element individual is optimized on the basis of the (<inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-1)-element individual to speed up the optimal solution search process. Experimental results on ten real-world networks demonstrate that the proposed algorithm SSR-PEA can achieve 98<inline-formula> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> of the influence spread achieved by cost-effective lazy forward (CELF) on average, and its running time is two or even three orders of magnitude shorter. Thus, SSR-PEA strikes a better balance between effectiveness and efficiency.

Link prediction for ex ante influence maximization on temporal networks

Influence maximization (IM) is the task of finding the most important nodes in order to maximize the spread of influence or information on a network. This task is typically studied on static or temporal networks where the complete topology of the graph is known. In practice, however, the seed nodes must be selected before observing the future evolution of the network. In this work, we consider this realistic ex ante setting where p time steps of the network have been observed before selecting the seed nodes. Then the influence is calculated after the network continues to evolve for a total of T>p time steps. We address this problem by using statistical, non-negative matrix factorization and graph neural networks link prediction algorithms to predict the future evolution of the network, and then apply existing influence maximization algorithms on the predicted networks. Additionally, the output of the link prediction methods can be used to construct novel IM algorithms. We apply the proposed methods to eight real-world and synthetic networks to compare their performance using the susceptible-infected (SI) diffusion model. We demonstrate that it is possible to construct quality seed sets in the ex ante setting as we achieve influence spread within 87% of the optimal spread on seven of eight network. In many settings, choosing seed nodes based only historical edges provides results comparable to the results treating the future graph snapshots as known. The proposed heuristics based on the link prediction model are also some of the best-performing methods. These findings indicate that, for these eight networks under the SI model, the latent process which determines the most influential nodes may not have large temporal variation. Thus, knowing the future status of the network is not necessary to obtain good results for ex ante IM.

Exploiting community and structural hole spanner for influence maximization in social networks

AbstractViral marketing is a frequently used social marketing strategy which aims to promote products on various social media. In order to devise an efficient viral marketing strategy, influence maximization problem is widely studied in social networks. Influence maximization problem tries to find a set of influential users who could influence social users maximally. However, existed influence maximization algorithms could not satisfy the needs of social marketers well. In social networks, community structure is an important feature where social users are closely connected together in groups, and structural hole spanners are those users who bridge different communities. In order to balance the effectiveness and efficiency of viral marketing in social networks, in this paper, we present to exploit the community structure and structural hole spanners in social networks for solving the influence maximization problem. Different to traditional algorithms, we devise a strategy to approximate social influences of social users to find seeds efficiently. In particular, for an internal user inside a community in social networks, we utilize his social influence to members inside this community to approximate his social influence in the whole social network. For a structural hole spanner who bridges multiple communities, we utilize his social influence to members in these communities to approximate his social influence in the whole network. Based on the approximate social influence, information diffusion model and greedy framework, we propose a Community and Structural Hole Spanner based Greedy (CSHS‐G) algorithm which devises several influence lists to store social influences of users and fast computation scheme to find seeds. Besides, to further improve the efficiency, we propose a Community and Structural Hole Spanner based Heuristic (CSHS‐H) algorithm which approximates social influences of structural hole spanners by utilizing their 2‐hops influences. We conduct a comprehensive performance evaluation on the crawled real‐world data set. Experimental results show that, compared to all of the baseline algorithms, our proposed algorithms not only have high efficiency, but also could guarantee larger influence spread.

Social learning-integrated flower pollination algorithm for influence maximization

Social learning-integrated flower pollination algorithm (SLFPA) is a solution to issues that meta-heuristic algorithms face when solving the influence maximization problem. These issues include the high probability of entrapment in local optima, a decrease in population diversity during later iterations, and low accuracy of solution. In human society, people often learn from others behavior. This mechanism of social learning is incorporated into the flower pollination algorithm. A global pollination strategy is devised to increase population diversity and avoid being trapped in local optima, which utilizes both the global optimal individual and the most improved individual. To enhance the accuracy of the algorithm, we have developed a local pollination strategy that involves creating a learning object based on close friends. We tested the proposed algorithm on six real social networks and compared it to six other advanced heuristic algorithms, and the results demonstrate the effectiveness of algorithm and improved the accuracy of the solution.