Methods for Influence Maximization in Dynamic Networks

Using swarm intelligence algorithms to detect influential individuals for influence maximization in social networks

Social networks currently serve as a primary platform for numerous connected intelligent individuals to share opinions and forward messages, which not only accelerate the diffusion of trending useful information but also facilitate the spreading of rumors and the execution of malicious attacks. Therefore, it is of crucial importance to understand how information diffuses in social networks. Most existing works either adopt empirical machine learning methods, which heavily rely on the quality and quantity of datasets, or develop mathematical dynamic models, which often neglect micro-interactions among users and the effects of time delays caused by users receiving information. In this paper, we propose an explainable framework to analyze information diffusion in social networks, which leverages the graphical evolutionary game theory to model scenarios where users receive and process information at varying rates. We define three types of time delay, model the micro-interaction among users, derive the dynamics of information diffusion, and analyze the conditions of system stability. We run simulations over both synthetic networks and three real-world social networks to validate the correctness of the proposed model. This work can provide a new perspective of modeling and predicting the information diffusion processes with time delays in different scenarios.

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.

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.

Social network is the mainstream medium of current information dissemination, and it is particularly important to accurately predict its propagation law. In this paper, we introduce a social network propagation model integrating multiple linear regression and infectious disease model. Firstly, we proposed the features that affect social network communication from three dimensions. Then, we predicted the node influence via multiple linear regression. Lastly, we used the node influence as the state transition of the infectious disease model to predict the trend of information dissemination in social networks. The experimental results on a real social network dataset showed that the prediction results of the model are consistent with the actual information dissemination trends.

SummaryOnline social networks play a pivotal role in the propagation of information and influence as in the form of word‐of‐mouth spreading. The influence maximization (IM) problem is a fundamental problem to identify a small set of individuals, which have a maximal influence spread in the social network. Unfortunately, the IM problem is NP‐hard. It has been depicted that a hill‐climbing greedy approach gives a good approximation guarantee. However, it is inefficient to run on large‐scale social networks. In this paper, a global influence evaluation function is presented for the IM optimization problem. The global influence evaluation function provides a reliable expected diffusion value of influence spread under the traditional diffusion models. To optimize global influence evaluation function, an influence maximization algorithm based on social spider optimization (IM‐SSO) is presented. IM‐SSO redefines the representation and update rule of spider's vibration and performs random walk towards target vibration. The algorithm uses a jump away process to overcome the weakness of premature convergence. The experimental results on six real‐world social networks show that the proposed algorithm is more effective than the state‐of‐the‐art heuristics and more time‐efficient than CELF++, static greedy, and PSO with an approximate influence spread.

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.

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 information dissemination in social networks is affected by many factors. However, node attitude which is an important influence factor of information dissemination in social network have not been fully considered in the previous works. Aiming at the problem of the influence of node attitude on information dissemination, this paper proposes an information propagation model based on evolutionary game. Firstly, from the individual point of view, the node’s attitude update rules are defined according to non-Bayesian social learning rules. Secondly, an inter-node game matrix based on attitude value is established. Based on the evolution analysis paradigm, an information dissemination model based on node attitude is established. The equilibrium solution of dynamic equations is replicated for both positive and negative attitudes, and the corresponding equilibrium points are stabilized. The validity of the proposed model is verified by numerical analysis and simulation experiments. They all show that the different attitudes of nodes play an important role in information dissemination.

In parallel with the development of online social networks, the number of active users in these media is increased, which mainly use these media as a tool to share their opinions and obtaining information. Propagation of influence on social networks arises from a common social behavior called "mouth-to-mouth" diffusion among society members. The Influence Maximization (IM) problem aims to select a minimum set of users in a social network to maximize the spread of influence. In this paper, we propose a method in order to solve the IM problem on social media that uses the network embedding concept to learn the feature vectors of nodes. In the first step of the proposed method, we extract a structural feature vector for each node by network embedding. Afterward, according to the similarity between the vectors, the seed set of influential nodes is selected in the second step. The investigation of the results obtained from applying the proposed method on the real datasets indicates its significant advantage against its alternatives. Specifically, the two properties of being submodular and monotonic in the proposed method, which lead to an optimal solution with the ratio of (1-1/e) approximation, make this method considered a tool with high potential in order to address the IM problem.

<span lang="EN-US">Social networks provide a fairly wide range of data that allows one way or another to evaluate the effect of the dissemination of information. This article presents the results of a study that describes methods for determining the key parameters of the model needed to analyze and predict the dissemination of information in social networks. An approach based on the analysis of statistical data on user behavior in social networks is proposed. The process of evaluating the main features of the model is described, including the mathematical methods used for data analysis and information dissemination modeling. The study aims to understand the processes of information dissemination in social networks and develop recommendations for the effective use of social networks as a communication and brand promotion tool, as well as to consider the analytical properties of the classical susceptible-infected-removed (SIR) model and evaluate its applicability to the problem of information dissemination. The results of the study can be used to create algorithms and techniques that will effectively manage the process of information dissemination in social networks.</span>

Viral marketing campaigns target primarily those individuals who are central in social networks and hence have social influence. Marketing events, however, may attract diverse audience. Despite the importance of event marketing, the influence of heterogeneous target groups is not well understood yet. In this paper, we define the Audience Selection (AS) problem in which different sets of agents need to be evaluated and compared based on their social influence. A typical application of Audience selection is choosing locations for a series of marketing events. The Audience selection problem is different from the well-known Influence Maximization (IM) problem in two aspects. Firstly, it deals with sets rather than nodes. Secondly, the sets are diverse, composed by a mixture of influential and ordinary agents. Thus, Audience selection needs to assess the contribution of ordinary agents too, while IM only aims to find top spreaders. We provide a systemic test for ranking influence measures in the Audience Selection problem based on node sampling and on a novel statistical method, the Sum of Ranking Differences. Using a Linear Threshold diffusion model on two online social networks, we evaluate eight network measures of social influence. We demonstrate that the statistical assessment of these influence measures is remarkably different in the Audience Selection problem, when low-ranked individuals are present, from the IM problem, when we focus on the algorithm’s top choices exclusively.

GAWF: Influence maximization method based on graph attention weight fusion

Information diffusion has been a crucial issue in social network research. The influence maximization problem asks for ways to identify nodes that are able to maximally diffuse information through a network. Recently, game-theoretical methods emerged that partitions a network into coalitions, and facilitate influence maximization. A notable example is a method based on Shapley value [13]. A major disadvantage with this approach is the lack of consideration of externality on coalition formation. In this paper, we propose consensus value for influence maximization (CVIM) to overcome this limitation. After forming coalitions using consensus value, the method selects initial coalitions based on the gain of each coalition, and finally chooses seed nodes in the selected coalitions. Empirical evidence over several real-world networks demonstrates that CVIM produces better results of influence maximization while significantly reducing the running time as compared to existing approaches.

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.