GAWF: Influence maximization method based on graph attention weight fusion

The process of rumor spreading among people can be represented as information diffusion in social network. The scale of rumor spread changes greatly depending on starting vertices. If we can select vertices that contribute to large scale diffusion, the vertices are expected to be important for viral marketing. Given a network and the size of the starting vertices, the problem of selecting vertices for maximizing information diffusion is called as influence maximization problem. We propose three new approximation methods for influence maximization problem in dynamic networks. These methods are the extensions of previous methods for static networks to dynamic networks. Experiments for comparing the performance show that our proposed method achieves 1.5 times as much in the scale of diffusion and approximately 7.8 times faster in computational time at the maximum compared with previous heuristic methods.

User recommendation systems enhance user engagement by encouraging users to act as inviters to interact with other users (invitees), potentially fostering information propagation. Conventional recommendation methods typically focus on modeling interaction willingness. Influence-Maximization (IM) methods focus on identifying a set of users to maximize the information propagation. However, existing methods face two significant challenges. First, recommendation methods fail to unleash the candidates' spread capability. Second, IM methods fail to account for the willingness to interact. To solve these issues, we propose two models named HeteroIR and HeteroIM. HeteroIR provides an intuitive solution to unleash the dissemination potential of user recommendation systems. HeteroIM fills the gap between the IM method and the recommendation task, improving interaction willingness and maximizing spread coverage. The HeteroIR introduces a two-stage framework to estimate the spread profits. The HeteroIM incrementally selects the most influential invitee to recommend and rerank based on the number of reverse reachable (RR) sets containing inviters and invitees. RR set denotes a set of nodes that can reach a target via propagation. Extensive experiments show that HeteroIR and HeteroIM significantly outperform the state-of-the-art baselines with the p-value<0.05. Furthermore, we have deployed HeteroIR and HeteroIM in Tencent's online gaming platforms and gained an 8.5% and 10% improvement in the online A/B test, respectively. Implementation codes are available at https://github.com/socialalgo/HIM.

The popularity of social networks has grown manifolds in recent years because of various activities like fast propagation of ideas, publicity, and news. Influence maximization (IM) is one of the most highly studied problems in the field of social network analysis due to its business values. Influence maximization aims to identify influential nodes that can spread the information to the maximum number of nodes in the network through diffusion cascade. Traditional methods for IM include centrality based and greedy based measures. However, each method has some limitations. Recently, some methods of IM are introduced, which consider the presence of community structure in networks. Community structure has a significant impact on information diffusion, because of dense connections between the nodes in the community. In this paper, we propose a novel influence maximization algorithm using node seeding, label propagation, and community detection. We first use extended h-index centrality to detect the seed nodes and then use the label propagation technique to detect communities. Further, we merge smaller and related communities to a larger community with the help of a relationship matrix. Finally, top-k influential nodes from these communities are identified. These ideas lead to our proposed algorithm: Influence Maximization using Extended h-index, and Label Propagation with Relationship matrix (IM-ELPR). We adopt Independent Cascade (IC) information diffusion model to spread the information originating from chosen influential nodes. The proposed algorithm intends to identify influential nodes from different communities globally and does not depend on the specific community’s antecedent structural information. Experimental results performed on several real-life data sets reveal that the proposed algorithm performs better than many other existing popular algorithms.

Influence maximization is one of the most fundamental problems in social network analysis due to its significant impact on viral marketing and targeted advertisements. Considerable amount of works has extensively studied to analyze the influence in social networks, but most of the existing works unfortunately neglected the fact that the location information in the cyber-physical world could also play an important role in the influence prorogation. Furthermore, even though a few works consider a little location information to enhance the influence maximization, they do not discuss any privacy issue of the model and expose user's location information directly to the public. This paper considers the problem of influence maximization in both GPS-enabled cyber-physical and online social networks with privacy reservation. We propose one novel model merging both GPS data of cyber-physical network and relationship data of online social network together in a unified framework, then we provide an efficient algorithm to solve the influence maximization problem in the framework. Besides the influence maximization problem, our framework could also support other applications involving both cyber-physical and online social networks. Further more, to protect the sensitive location and link information, we also provide corresponding techniques to protect the privacy during the whole influence maximization process. Empirical studies of real life datasets demonstrate the power of engaging location information to influence maximization, and suggest that our resolution outperforming most existing alternative algorithms with the protection of location privacy.

Influence Extremal Optimization (InfEO) is an algorithm based on Extremal Optimization, adapted for the influence maximization problem for the independent cascade model. InfEO maximizes the marginal contribution of a node to the influence set of the model. Numerical experiments are used to compare InfEO with other influence maximization methods, indicating the potential of this approach. Practical results are discussed on a network constructed from publication data in the field of computer science.

Most of the recent online social media collects a huge volume of data not just about who is linked with whom (aka link data) but also, about who is interacting with whom (aka interaction data). The presence of both variety and volume in these datasets pose new challenges while conducting social network analysis. In particular, we present a general framework to deal with both variety and volume in the data for a key social network analysis task - Influence Maximization. The well known influence maximization problem [15] (or viral marketing through social networks) deals with selecting a few influential initial seeds to maximize the awareness of product(s) over the social network. As it is computationally hard [15], a greedy approximation algorithm is designed to address the influence maximization problem. However, the major drawback of this greedy algorithm is that it runs extremely slow even on network datasets consisting of a few thousand nodes and edges [20,6]. Several efficient heuristics have been proposed in the literature [6] to alleviate this computational difficulty; however these heuristics are designed for specific influence propagation models such as linear threshold model and independent cascade model. This motivates the strong need to design an approach that not only works with any influence propagation model, but also efficiently solves the influence maximization problem. In this paper, we precisely address this problem by proposing a new framework which fuses both link and interaction data to come up with a backbone for a given social network, which can further be used for efficient influence maximization. We then conduct thorough experimentation with several real life social network datasets such as DBLP, Epinions, Digg, and Slashdot and show that the proposed approach is efficient as well as scalable.KeywordsSocial networksinfluence maximizationviral marketingsparsification

The connection between users in social networks can be maintained for a certain period of time, and the static network structure formed provides the basic conditions for various kinds of research, especially for discovering customer groups that can generate great influence, which is important for product promotion, epidemic prevention and control, and public opinion supervision, etc. However, the computational process of influence maximization ignores the timeliness of interaction behaviors among users, the screened target users cannot diffuse information well, and the time complexity of relying on greedy rules to handle the influence maximization problem is high. Therefore, this paper analyzes the influence of the interaction between nodes in dynamic social networks on information dissemination, extends the classical independent cascade model to a dynamic social network dissemination model based on effective links, and proposes a two-stage influence maximization solution algorithm (Outdegree Effective Link—OEL) based on node degree and effective links to enhance the efficiency of problem solving. In order to verify the effectiveness of the algorithm, five typical influence maximization methods are compared and analyzed on four real data sets. The results show that the OEL algorithm has good performance in propagation range and running time.

In recent years, Influence Maximization (IM) has gained great research interest in the field of social network research. The IM is a viral marketing based approach to find the influential users on the social networks. It determines a small seed set that can activate a maximum number of nodes in the network under some diffusion models such as Linear Threshold model or Independent Cascade model. However, previous works have not focused on the opportunity cost defined by the minimum number of nodes that must be motivated in order to activate the initial seed nodes. In this work, we have introduced a Reverse Influence Maximization (RIM) problem to estimate the opportunity cost. The RIM, working in opposite manner to IM, calculates the opportunity cost for viral marketing in the social networks. We have proposed the Extended Randomized Linear Threshold RIM (ERLT-RIM) model to solve the RIM problem. The ERLT-RIM is a Linear Threshold (LT)-based model which is an extension to the existing RLT-RIM model. We also have evaluated the performance of the algorithm using three real-world datasets. The result shows that the proposed model determines the optimal opportunity cost with time efficiency as compared to existing models.

Online social networks (OSNs) have witnessed their prosperous developments in recent years. Based on the established relations among individuals in OSNs, ideas and opinions can be spread via a word-of-mouth effect. To exploit this effect, many companies have taken OSNs as the major advertising channels to promote their products, which has motivated substantial research on viral marketing. Among them, influence maximization, seed minimization, and profit maximization have been extensively studied in the past decades. These three problems are mainly studied in the non-adaptive setting in the literature, i.e., seed user selection phase does not involve any observations on influence propagation in reality. In this thesis, we extend profit maximization into a generalized version as target profit maximization and investigate these three problems in the adaptive setting, formulated as adaptive influence maximization, adaptive seed minimization, and adaptive target profit maximization respectively. Firstly, we study the adaptive influence maximization (IM) problem. Given a social network G and an integer k, the influence maximization problem asks for a seed set S of k nodes from G to maximize the expected number of nodes activated via an influence propagation. In the adaptive setting, the k seed nodes are selected in batches of equal size b, such that the i-th batch is identified after the actual influence results of the former i-1 batches are observed. We propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of 1-e^α(ε-1) with high probability, where ε∊(0, 1) is a user-specified parameter and α= 1-(1-1/b)^b is set by the batch size b. Our approach is based on a novel general framework AdaptGreedy which could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. In this regard, we design a novel non-adaptive IM algorithm called EPIC which not only provides strong expected approximation guarantee, but also presents superior performance compared with the existing IM algorithms. Meanwhile, we clarify some existing misunderstandings in recent work and shed light on further study of the adaptive IM problem. Subsequently, we consider the adaptive seed minimization (SM) problem. As a dual problem of influence maximization, the seed minimization problem asks for the minimum number of seed nodes to influence a required number η of users in a given social network G. In the adaptive setting, the seed nodes are selected in several batches, such that the choice of current batch may exploit information about the actual influence of the previous batches. We devise a novel algorithm, ASTI, which addresses the adaptive seed minimization problem in O (η(m+n)/ε^2 ln n) expected time and offers an approximation guarantee of (ln η+1)^2/((1-(1-1/b)^b)(1-1/e)(1-ε)) in expectation, where η is the targeted number of influenced nodes, b is size of each seed node batch, and ε∊(0, 1) is a user-specified parameter. To the best of our knowledge, ASTI is the first algorithm that provides such an approximation guarantee without incurring prohibitive computation overhead. Eventually, we explore the adaptive target profit maximization (TPM) problem. Given a social network G, the profit maximization (PM) problem asks for a set of seed nodes to maximize the profit, i.e., revenue of influence spread less the cost of seed selection. The TPM problem, which generalizes the PM problem, aims to select a subset of seed nodes from a given target user set T to maximize the profit. In the adaptive setting, the seed users are selected through multiple batches, such that the selection of current batch exploits the knowledge of actual influence in the previous batches. To acquire an overall understanding, we study adaptive TPM under the oracle model and the noise model, to which we propose ADG and AddATP algorithms with strong theoretical guarantees respectively. In addition, we propose the idea of hybrid error to better handle the sampling errors under the noise model and design a novel algorithm HATP that boosts the efficiency of AddATP significantly.

Influence maximization refers to selecting a small number of influential nodes in a given network to maximize the influence affected by the subset. In social network analysis and viral marketing, influence maximization is greatly significant. The greedy-based algorithm is time-consuming in estimating the expected influence diffusion of a given node set, which is unsuitable for large-scale network. The traditional heuristics often have the problem of low accuracy. In this study, in order to solve the influence maximization problem more effectively, a meta-heuristic discrete crow search algorithm (DCSA) using the intelligence of crow population is proposed. In DCSA, a new coding mechanism and discrete evolution rules are constructed. The degree-based initialization method and the random walk strategy are adopted to enhance the search ability. Moreover, according to the network topology, influential nodes Candidates are generated to avoid blindness in the process of crow search. Extensive experiments are conducted on six real-world social networks under independent cascade (IC) model, the results show that DCSA outperforms other state-of-the-art algorithms and obtains comparable influence diffusion results to CELF but with lower time complexity.

In recent years, due to the surge in popularity of social-networking web sites, considerable interest has arisen regarding influence maximization in social networks. Given a social network structure, the problem of influence maximization is to determine a minimum set of nodes that could maximize the spread of influences. With a large-scale social network, the efficiency and practicability of such algorithms are critical. Although many recent studies have focused on the problem of influence maximization, these works in general are time-consuming when a social network is large-scale. In this paper, we propose two novel algorithms, CDH-Kcut and Community and Degree Heuristic on Kcut/SHRINK, to solve the influence maximization problem based on a realistic model. The algorithms utilize the community structure, which significantly decreases the number of candidates of influential nodes, to avoid information overlap. The experimental results on both synthetic and real datasets indicate that our algorithms not only significantly outperform the state-of-the-art algorithms in efficiency but also possess graceful scalability.

The research of Influence maximization (IM) has always been a hot research topic in network analysis, which aims to find the most influential users in social networks to maximize the reach of influence. In recent year, many studies have focused on the problem of IM to improve efficiency by taking advantage of the small-scale community structures. However, the existing community-based methods only consider the number of nodes in a community and ignore the density of edge connections in a community. In addition, existing method can only be applied to non-overlapping community structures. In this paper, we propose community closeness-based influence maximization algorithm (CCIM) to select most influential nodes. CCIM considers the influence of point-to-point and point-to-community, reflecting the micro-level and meso-level influence. The experimental results on synthetic and three real datasets verify CCIM outperforms the state-of-the-art baselines.

Nowadays, we use social networks such as Twitter, Facebook, WeChat and Weibo as means to communicate with each other. Social networks have become so indispensable in our everyday life that we cannot imagine what daily life would be like without social networks. Through social networks, we can access friends’ opinions and behaviors easily and are influenced by them in turn. Thus, an effective algorithm to find the top-K influential nodes (the problem of influence maximization) in the social network is critical for various downstream tasks such as viral marketing, anticipating natural hazards, reducing gang violence, public opinion supervision, etc. Solving the problem of influence maximization in real-world propagation scenarios often involves estimating influence strength (influence probability between two nodes), which cannot be observed directly. To estimate influence strength, conventional approaches propose various humanly devised rules to extract features of user interactions, the effectiveness of which heavily depends on domain expert knowledge. Besides, they are often applicable for special scenarios or specific diffusion models. Consequently, they are difficult to generalize into different scenarios and diffusion models. Inspired by the powerful ability of neural networks in the field of representation learning, we designed a hierarchical generative embedding model (HGE) to map nodes into latent space automatically. Then, with the learned latent representation of each node, we proposed a HGE-GA algorithm to predict influence strength and compute the top-K influential nodes. Extensive experiments on real-world attributed networks demonstrate the outstanding superiority of the proposed HGE model and HGE-GA algorithm compared with the state-of-the-art methods, verifying the effectiveness of the proposed model and algorithm.

We address the problem of influence maximization when the social network is accompanied by diffusion cascades. In prior works, such information is used to compute influence probabilities, which is utilized by stochastic diffusion models in influence maximization. Motivated by the recent criticism on the effectiveness of diffusion models as well as the galloping advancements in influence learning, we propose IMINFECTOR (Influence Maximization with INFluencer vECTORs), a unified approach that uses representations learned from diffusion cascades to perform model-independent influence maximization that scales in real-world datasets. The first part of our methodology is a multi-task neural network that learns embeddings of nodes that initiate cascades (influencer vectors) and embeddings of nodes that participate in them (susceptible vectors). The norm of an influencer vector captures the ability of the node to create lengthy cascades and is used to estimate the expected influence spread and reduce the number of candidate seeds. In addition, the combination of influencer and susceptible vectors form the diffusion probabilities between nodes. These are used to reformulate the network as a bipartite graph and propose a greedy solution to influence maximization that retains the theoretical guarantees.We a pply our method in three sizable networks with diffusion cascades and evaluate it using cascades from future time steps. IMINFECTOR is able to scale in all of them and outperforms various competitive algorithms and metrics from the diverse landscape of influence maximization in terms of efficiency and seed set quality.

Influence Maximization aims to find the top-$(K)$ influential individuals to maximize the influence spread within a social network, which remains an important yet challenging problem. Proven to be NP-hard, the influence maximization problem attracts tremendous studies. Though there exist basic greedy algorithms which may provide good approximation to optimal result, they mainly suffer from low computational efficiency and excessively long execution time, limiting the application to large-scale social networks. In this paper, we present IMGPU, a novel framework to accelerate the influence maximization by leveraging the parallel processing capability of graphics processing unit (GPU). We first improve the existing greedy algorithms and design a bottom-up traversal algorithm with GPU implementation, which contains inherent parallelism. To best fit the proposed influence maximization algorithm with the GPU architecture, we further develop an adaptive K-level combination method to maximize the parallelism and reorganize the influence graph to minimize the potential divergence. We carry out comprehensive experiments with both real-world and sythetic social network traces and demonstrate that with IMGPU framework, we are able to outperform the state-of-the-art influence maximization algorithm up to a factor of 60, and show potential to scale up to extraordinarily large-scale networks.