Existing Influence Maximization Algorithms Research Articles

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.

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.

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.

AIGCrank: A new adaptive algorithm for identifying a set of influential spreaders in complex networks based on gravity centrality

The influence maximization problem in complex networks asks to identify a given size of seed spreaders set to maximize the number of expected influenced nodes at the end of the spreading process. This problem finds many practical applications in numerous areas such as information dissemination, epidemic immunity, and viral marketing. However, most existing influence maximization algorithms are limited by the “rich-club” phenomenon and are thus unable to avoid the influence overlap of seed spreaders. This work proposes a novel adaptive algorithm based on a new gravity centrality and a recursive ranking strategy, named AIGCrank, to identify a set of influential seeds. Specifically, the gravity centrality jointly employs the neighborhood, network location and topological structure information of nodes to evaluate each node’s potential of being selected as a seed. We also present a recursive ranking strategy for identifying seed nodes one-by-one. Experimental results show that our algorithm competes very favorably with the state-of-the-art algorithms in terms of influence propagation and coverage redundancy of the seed set.

An Influence Maximization Algorithm Based on Community-Topic Features for Dynamic Social Networks

Real social networks are huge and continue to expand rapidly. Most existing dynamic influence maximization (IM) algorithms are based on the node-to-node propagation model; hence, they have high time complexity and large storage space consumption. They usually reduce computational complexity using a sampling method while sacrificing the influence spread. In this paper, we propose a topic-aware community independent cascade (IC) model to reduce the complexity of dynamic IM without losing accuracy. The proposed model reduces the problem domain through community-level propagation, and then enhances the global features by integrating community structural features, community topic features, and time information into an IC model. We construct the data structure of the dynamic community index to avoid recalculation when the network grows. Based on the dynamic community index, we design a dynamic IM algorithm to quickly approximate the solution with the (1-1/e)-approximation guarantee. The experimental results on real social networks demonstrated that, compared with existing IM algorithms, the proposed algorithm had better stability and dynamic adaptability, higher computational efficiency, and less space consumption without reducing the approximation ratio and influence spread.

ComIM: A community-based algorithm for influence maximization under the weighted cascade model on social networks

Influence maximization (IM) is a problem of selecting k nodes from social networks to make the expected number of the active node maximum. Recently, with the popularity of Internet technology, more and more researchers have paid attention to this problem. However, the existing influence maximization algorithms with high accuracy are usually difficult to be applied to the large-scale social network. To solve this problem the paper proposes a new algorithm, called community-based influence maximization (ComIM). Its core idea is “divide and conquer”. In detail, this algorithm first utilizes the Louvain algorithm to divide the large-scale networks into some small-scale networks. Afterwards, the algorithm utilizes the one-hop diffusion value (ODV) and two-hop diffusion value (TDV) functions to calculate the influence of a node and select nodes on these small-scale networks, which can improve the accuracy of our proposed algorithm. By using the above methods, the paper proposes a community influence-estimating method called CDV, which can improve the efficiency of the algorithm. Experimental results on six real-world datasets demonstrate that our proposed algorithm outperforms all comparison algorithms when comprehensively considering the accuracy and efficiency.

LTHS: A heuristic algorithm based on local two-hop search strategy for influence maximization in social networks

Influence maximization is a classic network optimization problem, which has been widely used in the field of viral marketing. The influence maximization problem aims to find a fixed number of active nodes. After a specific propagation model, the number of active nodes reaches the maximum. However, the existing influence maximization algorithms are overly pursuing certain indicators of efficiency or accuracy, which cannot be well accepted by some researchers. This paper proposes an effective algorithm to balance the accuracy and efficiency of the influence maximization problem called local two-hop search algorithm (LTHS). The core of the proposed algorithm is a node not only be affected by one-hop neighbor nodes, but also by two-hop neighbor nodes. Firstly, this paper selects initial seed nodes according to the characteristics of the node degree. Generally, the high degree of nodes regards as influential nodes. Secondly, this paper proposes a node two-hop influence evaluate function called two-hop diffusion value (THDV), which can evaluate node influence more accurately. Furthermore, in order to seek higher efficiency, this paper proposes a method to reduce the network scale. This paper conducted full experiments on five real-world social network datasets, and compared with other four well-known algorithms. The experimental results show that the LTHS algorithm is better than the comparison algorithms in terms of efficiency and accuracy.

Influence Maximization Algorithm Based on Reverse Reachable Set

Most of the existing influence maximization algorithms are not suitable for large-scale social networks due to their high time complexity or limited influence propagation range. Therefore, a D-RIS (dynamic-reverse reachable set) influence maximization algorithm is proposed based on the independent cascade model and combined with the reverse reachable set sampling. Under the premise that the influence propagation function satisfies monotonicity and submodularity, the D-RIS algorithm uses an automatic debugging method to determine the critical value of the number of reverse reachable sets, which not only obtains a better influence propagation range but also greatly reduces the time complexity. The experimental results on the two real datasets of Slashdot and Epinions show that D-RIS algorithm is close to the CELF (cost-effective lazy-forward) algorithm and higher than RIS algorithm, HighDegree algorithm, LIR algorithm, and pBmH (population-based metaheuristics) algorithm in influence propagation range. At the same time, it is significantly better than the CELF algorithm and RIS algorithm in running time, which indicates that D-RIS algorithm is more suitable for large-scale social network.

Dynamic top-k influence maximization in social networks

The problem of top-k influence maximization is to find the set of k users in a social network that can maximize the spread of influence under certain influence propagation model. This paper studies the influence maximization problem together with network dynamics. For example, given a real-life social network that evolves over time, we want to find k most influential users on everyday basis. This dynamic influence maximization problem has wide applications in practice. However, to our best knowledge, there is little prior work that studies this problem. Applying existing influence maximization algorithms at every time step provides a straightforward solution to the dynamic top-k influence maximization problem. Such a solution is, however, inefficient as it completely ignores the smoothness of network change. By analyzing two real social networks, Brightkite and Gowalla, we observe that the top-k influential set, as well as its influence value, does not change dramatically over time. Hence, it is possible to find the new top-k influential set by updating the previous one. We propose an efficient incremental update framework that takes advantage of such smoothness of network change. The proposed method achieves the same approximation ratio of 1 − e− 1 as its state-of-the-art static counterparts. Our experiments show that the proposed method outperforms the straightforward solution by a wide margin.

Efficient approximation algorithms for adaptive influence maximization

Given a social network $G$ and an integer $k$, the influence maximization (IM) problem asks for a seed set $S$ of $k$ nodes from $G$ to maximize the expected number of nodes influenced via a propagation model. The majority of the existing algorithms for the IM problem are developed only under the non-adaptive setting, i.e., where all $k$ seed nodes are selected in one batch without observing how they influence other users in real world. In this paper, we study the adaptive IM problem where 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. In this paper, we propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of $1-\mathrm{e}^{\rho_b(\varepsilon-1)}$, where $\rho_b=1-(1-1/b)^b$ and $\varepsilon \in (0, 1)$ is a user-specified parameter. In particular, we propose a general framework AdaptGreedy that could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. Our approach is based on a novel randomized policy that is applicable to the general adaptive stochastic maximization problem, which may be of independent interest. In addition, we propose 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. We conduct experiments on real social networks to evaluate our proposed algorithms comprehensively, and the experimental results strongly corroborate the superiorities and effectiveness of our approach.

Efficient algorithms for budgeted influence maximization on massive social networks

Given a social network G , a cost associated with each node, and a budget B , the budgeted influence maximization (BIM) problem aims to find a set S of nodes, denoted as the seed set, that maximizes the expected number of influenced users under the constraint that the total cost of the users in S is no larger than B. The current state-of-the-art practical solution for BIM problem provides a (1-1/ e /2 --- ε)-approximate (≈ 0.316 --- ε) result and is still inefficient on large networks. We first show that we can improve the approximation guarantee to 1 --- 1/ e β --- ε where 1 --- 1/ e β = (1 --- β) (1 --- 1/ e ), achieving a better approximation guarantee (≈ 0.355 --- ε). Next, we apply the reverse sampling based technique, a popular technique for classic influence maximization, to our studied BIM problem. However, it is non-trivial to design efficient solutions for large scale networks even the reverse sampling based technique is applied. On one hand, it is unclear how to derive tight bounds for the nodes selected by the greedy algorithm under the budgeted scenario, where each time it selects the seed node with the highest benefit-cost ratio. With tighter bounds, the algorithm can terminate as soon as the approximation ratio is satisfied, thus saving the running cost. On the other hand, the number of nodes selected under BIM problem may be quite large since it may greedily select many nodes with large benefit-cost ratio but with low costs. The time complexity of existing influence maximization algorithms heavily depends on the size of the seed set. To tackle such challenging issues, we first present new bound estimation techniques for the BIM problem. Next, we present new node selection strategies to alleviate the dependency to the size of the seed set. Extensive experiments show that our proposed solution is far more efficient than alternatives.

Recurrent neural variational model for follower-based influence maximization

Influence Maximization, aiming at selecting a small set of seed users in a social network to maximize the spread of influence, has attracted considerable attention recently. Most of the existing influence maximization algorithms focus on the diffusion model of one single-entity, which assumes that only one entity is propagated by users in social network. However, the diffusion situations in real world social networks often involve multiple entities, competitive or complementary, spreading through the whole network, and are more complex than the situations of single independent entity.In this paper, we propose a novel optimization problem, namely, the follower-based influence maximization, which aims to promote a new product into the market by maximizing the influence of a social network where other competitive and complementary products have already been propagating. We tackle this problem by proposing a Recurrent Neural Variational model (RNV) and a follower-based greedy algorithm (RNVGA). The RNV model dynamically tracks entity correlations and cascade correlations through a deep generative model and recurrent neural variational inference, while the RNVGA algorithm applies the greedy approach for submodular maximization and efficiently computes the seed node set for the target product. Extensive experiments have been conducted to evaluate effectiveness and efficiency of our method, and the results show the superiority of our method compared with the state-of-the-art methods.

Targeted Influence Maximization Based on Cloud Computing Over Big Data in Social Networks

This paper focuses on the targeted influence maximization based on cloud computing in social networks. Most of existing influence maximization works assume that the influence diffusion probabilities on edges are fixed, and identify the Top-k users to maximize the spread of influence assuming the knowledge of the entire network graph. However, in real-world scenarios, edge probabilities are typically different based on various topics, and may be affected by information received. Meanwhile, obtaining complete network data is difficult due to privacy and computational considerations. Moreover, existing influence maximization algorithms considering target users do not discuss cloud computing which lead to low computational efficiency when dealing with big datasets in social networks. To this end, this paper proposes a targeted influence maximization solution based on cloud computing. First, a new topic-aware model called tag-aware IC model is presented, which takes into account users' interests, characteristics of the item being propagated, and the similarity between users and the related information. Then, efficient algorithms with approximation guarantee are provided using a bounded number of queries to the graph structure. These methods aim to find a seed set that maximizes the expected influence spread over target users who are relevant to given topics. Finally, empirical studies of the proposed algorithms are designed and performed on real datasets. The experimental results show that the techniques in this paper achieves speedup and savings in storage compared with the state-of-the-art methods.

Community-based influence maximization in attributed networks

Influence Maximization, aiming at selecting a small set of seed users in a social network to maximize the spread of influence, has attracted considerable attention recently. Most existing influence maximization algorithms focus on pure networks, while in many real-world social networks, nodes are often associated with a rich set of attributes or features, aka attributed networks. Moreover, most of existing influence maximization methods suffer from the problems of high computational cost and no performance guarantee, as these methods heavily depend on analysis and exploitation of network structure. In this paper, we propose a new algorithm to solve community-based influence maximization problem in attributed networks, which consists of three steps: community detection, candidate community generation and seed node selection. Specifically, we first propose the candidate community generation process, which utilizes information of community structure as well as node attribute to narrow down possible community candidates. We then propose a model to predict influence strength between nodes in attributed network, which takes advantage of topology structure similarity and attribute similarity between nodes in addition to social interaction strength, thus improve the prediction accuracy comparing to the existing methods significantly. Finally, we select seed nodes by proposing the computation method of influence set, through which the marginal influence gain of nodes can be calculated directly, avoiding tens of thousands of Monte Carlo simulations and ultimately making the algorithm more efficient. Experiments on four real social network datasets demonstrate that our proposed algorithm outperforms state-of-the-art influence maximization algorithms in both influence spread and running time.

Location-aware Influence Maximization over Dynamic Social Streams

Influence maximization (IM), which selects a set of k seed users (a.k.a., a seed set ) to maximize the influence spread over a social network, is a fundamental problem in a wide range of applications. However, most existing IM algorithms are static and location-unaware. They fail to provide high-quality seed sets efficiently when the social network evolves rapidly and IM queries are location-aware. In this article, we first define two IM queries, namely Stream Influence Maximization (SIM) and Location-aware SIM (LSIM), to track influential users over social streams. Technically, SIM adopts the sliding window model and maintains a seed set with the maximum influence value collectively over the most recent social actions. LSIM further considers social actions are associated with geo-tags and identifies a seed set that maximizes the influence value in a query region over a location-aware social stream. Then, we propose the Sparse Influential Checkpoints (SIC) framework for efficient SIM query processing. SIC maintains a sequence of influential checkpoints over the sliding window and each checkpoint maintains a partial solution for SIM in an append-only substream of social actions. Theoretically, SIC keeps a logarithmic number of checkpoints w.r.t. the size of the sliding window and always returns an approximate solution from one of the checkpoint for the SIM query at any time. Furthermore, we propose the Location-based SIC (LSIC) framework and its improved version LSIC + , both of which process LSIM queries by integrating the SIC framework with a Quadtree spatial index. LSIC can provide approximate solutions for both ad hoc and continuous LSIM queries in real time, while LSIC + further improves the solution quality of LSIC. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of the proposed frameworks against the state-of-the-art IM algorithms.

Influence Maximization on Social Graphs: A Survey

Influence Maximization (IM), which selects a set of $k$ users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem in social influence analysis. Due to its immense application potential and enormous technical challenges, IM has been extensively studied in the past decade. In this paper, we survey and synthesize a wide spectrum of existing studies on IM from an algorithmic perspective , with a special focus on the following key aspects: (1) a review of well-accepted diffusion models that capture the information diffusion process and build the foundation of the IM problem, (2) a fine-grained taxonomy to classify existing IM algorithms based on their design objectives, (3) a rigorous theoretical comparison of existing IM algorithms, and (4) a comprehensive study on the applications of IM techniques in combining with novel context features of social networks such as topic, location, and time. Based on this analysis, we then outline the key challenges and research directions to expand the boundary of IM research.

Efficient algorithms for adaptive influence maximization

Given a social network G , the influence maximization (IM) problem seeks a set S of k seed nodes in G to maximize the expected number of nodes activated via an influence cascade starting from S. Although a lot of algorithms have been proposed for IM, most of them only work under the non-adaptive setting, i.e., when all k seed nodes are selected before we observe how they influence other users. In this paper, we study the adaptive IM problem, where we select the k seed nodes in batches of equal size b , such that the choice of the i -th batch can be made after the influence results of the first i - 1 batches are observed. We propose the first practical algorithms for adaptive IM with an approximation guarantee of 1 − exp(ξ − 1) for b = 1 and 1 − exp(ξ − 1 + 1/ e ) for b > 1, where ξ is any number in (0, 1). Our approach is based on a novel AdaptGreedy framework instantiated by non-adaptive IM algorithms, and its performance can be substantially improved if the non-adaptive IM algorithm has a small expected approximation error. However, no current non-adaptive IM algorithms provide such a desired property. Therefore, we further propose a non-adaptive IM algorithm called EPIC, which not only has the same worst-case performance bounds with that of the state-of-the-art non-adaptive IM algorithms, but also has a reduced expected approximation error. We also provide a theoretical analysis to quantify the performance gain brought by instantiating AdaptGreedy using EPIC, compared with a naive approach using the existing IM algorithms. Finally, we use real social networks to evaluate the performance of our approach through extensive experiments, and the experimental experiments strongly corroborate the superiorities of our approach.