Influence Maximization Algorithm Research Articles

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 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.

Influence Maximization in Complex Networks by Using Evolutionary Deep Reinforcement Learning

Influence maximization (IM) in complex networks tries to activate a small subset of seed nodes that could maximize the propagation of influence. The studies on IM have attracted much attention due to their wide applications such as item recommendation, viral marketing, information propagation and disease immunization. Existing works mainly model the IM problem as a discrete optimization problem, and use either approximate or meta-heuristic algorithms to address this problem. However, these works are hard to find a good tradeoff between effectiveness and efficiency due to the NP-hard and large-scale network properties of the IM problem. In this article, we propose an evolutionary deep reinforcement learning algorithm (called EDRL-IM) for IM in complex networks. First, EDRL-IM models the IM problem as a continuous weight parameter optimization of deep Q network (DQN). Then, it combines an evolutionary algorithm (EA) and a deep reinforcement learning algorithm (DRL) to evolve the DQN. The EA simultaneously evolves a population of individuals, and each of which represents a possible DQN and returns a solution to the IM problem through a dynamic markov node selection strategy, while the DRL integrates all information and network-specific knowledge of DQNs to accelerate their evolution. Systematic experiments on both benchmark and real-world networks show the superiority of EDRL-IM over the state-of-the-art IM methods in finding seed nodes.

K＋＋ Shell: Influence maximization in multilayer networks using community detection

Selecting influential users in a network is essential to spread information quickly. Identifying influential users is very useful for viral marketing and brand communication. Influence maximization (IM) is selecting a few influential users in the network who can maximize the influence spread. Many existing algorithms address IM in single-layer networks. However, the study of IM in multi-layer networks is gaining importance after the advancement and rapid growth in the usage of online social networks. Studying IM in multi-layer networks in the context of viral marketing will be interesting. Motivated by this, this paper investigates the K＋＋ Shell decomposition algorithm to find the k set of influential nodes (seed nodes) in a multi-layer network. The proposed model prunes the nodes based on degree and assign reward points to their neighbors. We conducted a comparative study of various IM algorithms and reported the results. We observed that the K＋＋ Shell decomposition algorithm outperforms other algorithms on various real-time datasets under various settings and environments.

A new community-based algorithm based on a “peak-slope-valley” structure for influence maximization on social networks

Influence Maximization (IM) is a key algorithmic problem that has been extensively studied in social influence analysis, but most of existing researches either make sacrifices in solution accuracy or suffer high computational complexity. In this paper, we propose a new Community-based Influence Maximization (CIM) algorithm for identifying a set of seed spreaders in a social network to maximize the expected number of influenced nodes. In CIM, the initial candidate seeds are first selected based on the proposed topological potential “peak-slope-valley” structure framework. Then, we propose a recursive clustering approach and a similarity indicator based on local resource allocation to partition communities. Finally, we design a community-based regional influence indicator to select seed nodes without using any prior knowledge. Experiment datasets include three artificial benchmarks with varying community strengths, as well as nine representative networks drawn from various fields. Extensive numerical simulations on both artificial and real networks indicate that (i) community-based techniques enrich the toolbox for addressing the IM problem and (ii) the derivative algorithm outperforms recent high-performing influence maximization algorithms in terms of influence propagation and coverage redundancy of the seed set with an acceptable complexity. Furthermore, our algorithm exhibits good stability on networks of varying scales and structural characteristics.

Community-Based Influence Maximization Using Network Embedding in Dynamic Heterogeneous Social Networks

Influence maximization (IM) is a very important issue in social network diffusion analysis. The topology of real social network is large-scale, dynamic, and heterogeneous. The heterogeneity, and continuous expansion and evolution of social network pose a challenge to find influential users. Existing IM algorithms usually assume that social networks are static or dynamic but homogeneous to simplify the complexity of the IM problem. We propose a community-based influence maximization algorithm using network embedding in dynamic heterogeneous social networks. We use DyHATR algorithm to obtain the propagation feature vectors of network nodes, and executek-means cluster algorithm to transform the original network into a coarse granularity network (CGN). On CGN, we propose a community-based three-hop independent cascade model and construct the objective function of IM problem. We design a greedy heuristics algorithm to solve the IM problem with\((1-\frac{1}{e})-\)approximation guarantee and use community structure to quickly identify seed users and estimate their influence value. Experimental results on real social networks demonstrated that compared with existing IM algorithms, our proposed algorithm had better comprehensive performance with respect to the influence value, more less execution time and memory consumption, and better scalability.

A fast module identification and filtering approach for influence maximization problem in social networks

In this paper, we explore influence maximization, one of the most widely studied problems in social network analysis. However, developing an effective algorithm for influence maximization is still a challenging task given its NP-hard nature. To tackle this issue, we propose the CSP (Combined modules for Seed Processing) algorithm, which aim to identify influential nodes. In CSP, graph modules are initially identified by a combination of criteria such as the clustering coefficient, degree, and common neighbors of nodes. Nodes with the same label are then clustered together into modules using label diffusion. Subsequently, only the most influential modules are selected using a filtering method based on their diffusion capacity. The algorithm then merges neighboring modules into distinct modules and extracts a candidate set of influential nodes using a new metric to quickly select seed sets. The number of selected nodes for the candidate set is restricted by a defined limit measure. Finally, seed nodes are chosen from the candidate set using a novel node scoring measure. We evaluated the proposed algorithm on both real-world and synthetic networks, and our experimental results indicate that the CSP algorithm outperforms other competitive algorithms in terms of solution quality and speedup on tested networks.

Robust Influence Maximization Under Both Aleatory and Epistemic Uncertainty

Uncertainty is ubiquitous in almost every real-life optimization problem, which must be effectively managed to get a robust outcome. This is also true for the Influence Maximization (IM) problem, which entails locating a set of influential users within a social network. However, most of the existing IM approaches have overlooked the uncertain factors in finding the optimal solution, which often leads to subpar performance in reality. A few recent studies have considered only the epistemic uncertainty (i.e., arises from the imprecise data), while ignoring completely the aleatory uncertainty (i.e., arises from natural or physical variability). In this article, we propose a formulation and a novel algorithm for the Robust Influence Maximization (RIM) problem under both types of uncertainties. First, we develop a robust influence spread function under aleatory uncertainty that, in contrast to the existing IM theory, is no longer monotone and submodular. Thereafter, we expand our RIM formulation to incorporate epistemic uncertainty aiming to maximize the robust ratio between the selected worst-case solution and the best-case optimal solution, adopting a conservative approach. Furthermore, using a chance-constraint-based method, we investigated feasibility robustness by accounting for the uncertainties related to constraint functions. Finally, an Evolutionary Algorithm (named EA-RIM) is designed to solve the proposed formulation of the RIM problem. Experimental evaluation results on four empirical datasets show that our proposed formulation and algorithm are more effective in dealing with uncertainties and finding an optimal solution for the RIM problem.

Triadic Closure Sensitive Influence Maximization

The influence are not linked to any footnote in the text. Please check and suggest. maximization problem aims at selecting the k most influential nodes (i.e., seed nodes) from a social network, where the nodes can maximize the number of influenced nodes activated by a certain propagation model. However, the widely used Independent Cascade model shares the same propagation probability among substantial adjacent node pairs, which is too idealistic and unreasonable in practice. In addition, most heuristic algorithms for influence maximization need to update the expected influence of the remaining nodes in the seed selection process, resulting in high computation cost. To address these non-trivial problems, we propose a novel edge propagation probability calculation method. The method first utilizes the triadic closure structure of social networks to precisely measure the closeness between nodes and assigns different propagation probabilities to each edge, deriving a Triadic Closure-based Independent Cascade (TC-IC) model. Then, we further propose a heuristic influence maximization algorithm named Triadic Closure-based Influence Maximization (TC-IM). The algorithm evaluates the expected influence of a node by integrating the triadic closure weighted propagation probability and the triadic closure weighted degree. Especially, in the seed selection process, only the most influential node that has not been updated in the current round needs to be updated, which significantly improves the efficiency. Besides, we further provide theoretical proofs to guarantee the correctness of this updating strategy. Experimental results on nine real datasets and three propagation models demonstrate that: (1) The TC-IC model can set a proper propagation probability for each node pair, where the IM algorithms could easily identify influential nodes; (2) The TC-IM algorithm can significantly reduce the complexity through an efficient updating strategy with a comparable influence spread to the approximation IM algorithms; (3) Besides, the TC-IM algorithm also exhibits stable performance under other IC models including UIC and WIC, exhibiting good stability and generality.