Influence Maximization Algorithm Research Articles

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.

A novel discrete ICO algorithm for influence maximization in complex networks

A novel discrete ICO algorithm for influence maximization in complex networks

Overlapping community‐based particle swarm optimization algorithm for influence maximization in social networks

AbstractInfluence maximization, whose aim is to maximise the expected number of influenced nodes by selecting a seed set of k influential nodes from a social network, has many applications such as goods advertising and rumour suppression. Among the existing influence maximization methods, the community‐based ones can achieve a good balance between effectiveness and efficiency. However, this kind of algorithm usually utilise the network community structures by viewing each node as a non‐overlapping node. In fact, many nodes in social networks are overlapping ones, which play more important role in influence spreading. To this end, an overlapping community‐based particle swarm optimization algorithm named OCPSO for influence maximization in social networks, which can make full use of overlapping nodes, non‐overlapping nodes, and their interactive information is proposed. Specifically, an overlapping community detection algorithm is used to obtain the information of overlapping community structures, based on which three novel evolutionary strategies, such as initialisation, mutation, and local search are designed in OCPSO for better finding influential nodes. Experimental results in terms of influence spread and running time on nine real‐world social networks demonstrate that the proposed OCPSO is competitive and promising comparing to several state‐of‐the‐arts (e.g. CGA, CMA‐IM, CIM, CDH‐SHRINK, CNCG, and CFIN).

An Influence Maximization Algorithm Based on Improved K-Shell in Temporal Social Networks

Influence maximization of temporal social networks (IMT) is a problem that aims to find the most influential set of nodes in the temporal network so that their information can be the most widely spread. To solve the IMT problem, we propose an influence maximization algorithm based on an improved K-shell method, namely improved K-shell in temporal social networks (KT). The algorithm takes into account the global and local structures of temporal social networks. First, to obtain the kernel value <i>Ks</i> of each node, in the global scope, it layers the network according to the temporal characteristic of nodes by improving the K-shell method. Then, in the local scope, the calculation method of comprehensive degree is proposed to weigh the influence of nodes. Finally, the node with the highest comprehensive degree in each core layer is selected as the seed. However, the seed selection strategy of KT can easily lose some influential nodes. Thus, by optimizing the seed selection strategy, this paper proposes an efficient heuristic algorithm called improved K-shell in temporal social networks for influence maximization (KTIM). According to the hierarchical distribution of cores, the algorithm adds nodes near the central core to the candidate seed set. It then searches for seeds in the candidate seed set according to the comprehensive degree. Experiments show that KTIM is close to the best performing improved method for influence maximization of temporal graph (IMIT) algorithm in terms of effectiveness, but runs at least an order of magnitude faster than it. Therefore, considering the effectiveness and efficiency simultaneously in temporal social networks, the KTIM algorithm works better than other baseline algorithms.

A Positive Influence Maximization Algorithm in Signed Social Networks

A Positive Influence Maximization Algorithm in Signed Social Networks

Finding Influencers in Complex Networks: An Effective Deep Reinforcement Learning Approach

Abstract Maximizing influences in complex networks is a practically important but computationally challenging task for social network analysis, due to its nondeterministic polynomial time (NP)-hard nature. Most current approximation or heuristic methods either require tremendous human design efforts or achieve unsatisfying balances between effectiveness and efficiency. Recent machine learning attempts only focus on speed but lack performance enhancement. In this paper, different from previous attempts, we propose an effective deep reinforcement learning model that achieves superior performances over traditional best influence maximization algorithms. Specifically, we design an end-to-end learning framework that combines graph neural network as the encoder and reinforcement learning as the decoder, named DREIM. Through extensive training on small synthetic graphs, DREIM outperforms the state-of-the-art baseline methods on very large synthetic and real-world networks on solution quality, and we also empirically show its linear scalability with regard to the network size, which demonstrates its superiority in solving this problem.

An efficient adaptive degree-based heuristic algorithm for influence maximization in hypergraphs

Influence maximization (IM) has shown wide applicability in immense fields over the past decades. Previous researches on IM mainly focused on the dyadic relationship but lacked the consideration of higher-order relationship between entities, which has been constantly revealed in many real systems. An adaptive degree-based heuristic algorithm, i.e., Hyper Adaptive Degree Pruning (HADP) which aims to iteratively select nodes with low influence overlap as seeds, is proposed in this work to tackle the IM problem in hypergraphs. Furthermore, we extend algorithms from ordinary networks as baselines. Results on 8 empirical hypergraphs show that HADP surpasses the baselines in terms of both effectiveness and efficiency with a maximally 46.02% improvement. Moreover, we test the effectiveness of our algorithm on synthetic hypergraphs generated by different degree heterogeneity. It shows that the improvement of our algorithm effectiveness increases from 2.66% to 14.67% with the increase of degree heterogeneity, which indicates that HADP shows high performance especially in hypergraphs with high heterogeneity, which is ubiquitous in real-world systems.

Algorithms for influence maximization in socio-physical networks

Given a directed graph (referred to as social network), the influence maximization problem is to find k nodes which, when influenced (or activated), would maximize the number of remaining nodes that get activated under a given set of activation dynamics. In this paper, we consider a more general version of the problem that includes an additional set (or layer) of nodes that are termed as physical nodes, such that a node in the social network is connected to one physical node. A physical node exists in one of two states at any time, opened or closed, and there is a constraint on the maximum number of physical nodes that can be opened. In this setting, an inactive node in the social network becomes active if it has at least one active neighbor in the social network and if it is connected to an opened physical node. This problem arises in scenarios such as disaster recovery, where a displaced social group (an inactive social node) decides to return back after a disaster (switches to active state) only after a sufficiently large number of groups in its social network return back and some infrastructure components (physical nodes) in its neighborhood are repaired (brought to the open state). We first show that this general problem is NP-hard to approximate within any constant factor. We then consider instances of the problem when the mapping between the social nodes and the physical nodes is bijective and characterize optimal and approximation algorithms for those instances.

Influence Maximization With Visual Analytics.

In social networks, individuals' decisions are strongly influenced by recommendations from their friends, acquaintances, and favorite renowned personalities. The popularity of online social networking platforms makes them the prime venues to advertise products and promote opinions. The Influence Maximization (IM) problem entails selecting a seed set of users that maximizes the influence spread, i.e., the expected number of users positively influenced by a stochastic diffusion process triggered by the seeds. Engineering and analyzing IM algorithms remains a difficult and demanding task due to the NP-hardness of the problem and the stochastic nature of the diffusion processes. Despite several heuristics being introduced, they often fail in providing enough information on how the network topology affects the diffusion process, precious insights that could help researchers improve their seed set selection. In this paper, we present VAIM, a visual analytics system that supports users in analyzing, evaluating, and comparing information diffusion processes determined by different IM algorithms. Furthermore, VAIM provides useful insights that the analyst can use to modify the seed set of an IM algorithm, so to improve its influence spread. We assess our system by: (i) a qualitative evaluation based on a guided experiment with two domain experts on two different data sets; (ii) a quantitative estimation of the value of the proposed visualization through the ICE-T methodology by Wall et al. (IEEE TVCG - 2018). The twofold assessment indicates that VAIM effectively supports our target users in the visual analysis of the performance of IM algorithms.

FIP: A fast overlapping community-based influence maximization algorithm using probability coefficient of global diffusion in social networks

Influence maximization is the process of identifying a small set of influential nodes from a complex network to maximize the number of activation nodes. Due to the critical issues such as accuracy, stability, and time complexity in selecting the seed set, many studies and algorithms has been proposed in recent decade. However, most of the influence maximization algorithms run into major challenges such as the lack of optimal seed nodes selection, unsuitable influence spread, and high time complexity. In this paper intends to solve the mentioned challenges, by decreasing the search space to reduce the time complexity. Furthermore, It selects the seed nodes with more optimal influence spread concerning the characteristics of a community structure, diffusion capability of overlapped and hub nodes within and between communities, and the probability coefficient of global diffusion. The proposed algorithm, called the FIP algorithm, primarily detects the overlapping communities, weighs the communities, and analyzes the emotional relationships of the community’s nodes. Moreover, the search space for choosing the seed nodes is limited by removing insignificant communities. Then, the candidate nodes are generated using the effect of the probability of global diffusion. Finally, the role of important nodes and the diffusion impact of overlapping nodes in the communities are measured to select the final seed nodes. Experimental results in real-world and synthetic networks indicate that the proposed FIP algorithm has significantly outperformed other algorithms in terms of efficiency and runtime.

TSIFIM: A three-stage iterative framework for influence maximization in complex networks

The problem of influence maximization is a classic issue that has been well-studied in the field of network science, but most of existing researches are compromising among computational complexity or result accuracy. In this work, a three-stage iterative framework for influence maximization (TSIFIM) is presented to find a set of seed spreaders in complex networks. In TSIFIM, the initial candidate seeds are first selected by considering the global communicability of each node and its importance in their local network. Then, in addition to the candidate seeds, other remained nodes are assigned to the specific communities based on the proposed local resource allocation similarity index, and the core node in each community which satisfies the local influence threshold condition are selected as the supplementary candidate seeds. Furthermore, we employ an adaptive search strategy to find the optimal solution among these candidates. The proposed algorithm is compared with eight popular influence maximization algorithms on nine real-world networks to verify the performance. Experimental results show that TSIFIM has better performance in terms of influence spreading, sensitivity analysis, seed dispersion and statistical test.

Influence maximization based on network representation learning in social network

Influence Maximization (IM), an NP-hard central issue for social network research, aims to recognize the influential nodes in a network so that the message can spread faster and more effectively. A large number of existing studies mainly focus on the heuristic methods, which generally lead to sub-optimal solutions and suffer time-consuming and inapplicability for large-scale networks. Furthermore, the present community-aware random walk to analyze IM using network representation learning considers only the node’s influence or network community structures. No research has been found that surveyed both of them. Hence, the present study is designed to solve the IM problem by introducing a novel influence network embedding (NINE) approach and a novel influence maximization algorithm, namely NineIM, based on network representation learning. First, a mechanism that can capture the diffusion behavior proximity between network nodes is constructed. Second, we consider a more realistic social behavior assumption. The probability of information dissemination between network nodes (users) is different from other random walk based network representation learning. Third, the node influence is used to define the rules of random walk and then get the embedding representation of a social network. Experiments on four real-world networks indicate that our proposed NINE method outperforms four state-of-the-art network embedding baselines. Finally, the superiority of the proposed NineIM algorithm is reported by comparing four traditional IM algorithms. The code is available at https://github.com/baiyazi/NineIM.

An improved clustering based multi-objective evolutionary algorithm for influence maximization under variable-length solutions

Knowledge of influential actors on real networks is essential for designing policies for boosting the spread of positive things (e.g., news and innovation) and preventing the spread of negative things (e.g., disease and misinformation). Finding an optimum set of nodes with maximum influence, known as Influence Maximization (IM), aims to achieve this, which requires consideration of both magnitude of the influence spread and other important factors such as the cost and size of the seed set. However, most previous research has viewed the IM problem as a single objective problem, wherein decision-makers are required to make decisions on other criteria without having a clear view of them. In this study, the IM problem is formulated as a Multi-objective Influence Maximization Problem (MIMP) with three conflicting objectives and real-world constraints. An improved version of θ-Dominance based Evolutionary Algorithm, named as θDEA-II, is proposed to solve the MIMP. To achieve a better balance between divergence and convergence of the proposed θDEA-II, a gap-based selection operator is introduced along with some modifications in the sorting and normalization process. Moreover, because the proposed MIMP deals with variable-length solutions, all of the investigated algorithms, including the baseline algorithms, are constructed with a novel crossover mechanism capable of producing offsprings that are different in size from their parents. Experimental results on six real-world datasets demonstrate that the proposed MIMP formulation as well as the θDEA-II algorithm are effective for finding an optimal solution.

Influence maximization in social networks using transfer learning via graph-based LSTM

Social networks have emerged as efficient platforms to connect people worldwide and facilitate the rapid spread of information. Identifying influential nodes in social networks to accelerate the spread of particular information across the network formulates the study of influence maximization (IM). In this paper, inspired by deep learning techniques, we propose a novel approach to solve the influence maximization problem as a classical regression task using transfer learning via graph-based long short-term memory (GLSTM). We start by calculating three popular node centrality methods as feature vectors for the nodes in the network and every node’s individual influence under susceptible–infected–recovered (SIR) information diffusion model, which forms the labels of the nodes in the network. The generated feature vectors and their corresponding labels for all the nodes are then fed into a graph-based long short-term memory (GLSTM). The proposed architecture is trained on a vast and complex network to generalize the model parameters better. The trained model is then used to predict the probable influence of every node in the target network. The proposed model is compared with some of the well-known and recently proposed algorithms of influence maximization on several real-life networks using the popular SIR model of information diffusion. The intensive experiments suggest that the proposed model outperforms these well-known and recently proposed influence maximization algorithms.