Influence Maximization Problem Research Articles

An influence model for influence maximization–revenue optimization

The rise of online social networks (OSNs) has caused an insurmountable amount of interest from advertisers and researchers seeking to monopolize on its features. Researchers aim to develop strategies for propagating information among users within an OSN that is captured by diffusion or influence models. Within the last decade, influence models have been extensively studied for the influence maximization (IM) problem. Recently, a novel stochastic dynamic programming (SDP) formulation to influence maximization called the influence maximization–revenue optimization (IM–RO) problem was proposed with numerous lucrative advantages. In this paper, we validate the intuition behind the proposed influence model for the IM–RO problem empirically. We focus on demonstrating the correctness of the notion behind the influence model that the more of a user’s friends who click on an advertisement, the more likely the user is to click on the advertisement themselves and use a decision tree regressor to predict this probability. To further support the premise of our influence model and estimate its parameters, we implement a linear regression and a Bayesian model. Results indicate that the linear regression model captures the functional relationship between its dependent and the independent variables. We extend the experiments to real-world OSNs and investigate additional predictor variables that influence the number of posts and reposts.

Positive Influence Maximization in the Signed Social Networks Considering Polarity Relationship and Propagation Probability

The purpose of influence maximization problem is to select a small seed set to maximize the number of nodes influenced by the seed set. For viral marketing, the problem of influence maximization plays a vital role. Current works mainly focus on the unsigned social networks, which include only positive relationship between users. However, the influence maximization in the signed social networks including positive and negative relationships between users is still a challenging issue. Moreover, the existing works pay more attention to the positive influence. Therefore, this paper first analyzes the positive maximization influence in the signed social networks. The purpose of this problem is to select the seed set with the most positive influence in the signed social networks. Afterwards, this paper proposes a model that incorporates the state of node, the preference of individual and polarity relationship, called Independent Cascade with the Negative and Polarity (ICWNP) propagation model. On the basis of the ICWNP model, this paper proposes a Greedy with ICWNP algorithm. Finally, on four real social networks, experimental results manifest that the proposed algorithm has higher accuracy and efficiency than the related methods.

Joint Selection of Influential Users and Locations under Target Region in Location-Based Social Networks.

Influence Maximization problem, selection of a set of users in a social network to maximize the influence spread, has received ample research attention in the social network analysis domain due to its practical applications. Although the problem has been extensively studied, existing works have neglected the location’s popularity and importance along with influential users for product promotion at a particular region in Location-based Social Networks. Real-world marketing companies are more interested in finding suitable locations and influential users in a city to promote their product and attract as many users as possible. In this work, we study the joint selection of influential users and locations within a target region from two complementary perspectives; general and specific location type selection perspectives. The first is to find influential users and locations at a specified region irrespective of location type or category. The second perspective is to recommend locations matching location preference in addition to the target region for product promotion. To address general and specific location recommendations and influential users, we propose heuristic-based methods that effectively find influential users and locations for product promotion. Our experimental results show that it is not always an optimal choice to recommend locations with the highest popularity values, such as ratings, check-ins, and so, which may not be a true indicator of location popularity to be considered for marketing. Our results show that not only influential users are helpful for product promotion, but suitable influential locations can also assist in promoting products in the target region.

Finding Influential Nodes in Multiplex Networks Using a Memetic Algorithm.

In order to find the nodes with better propagation ability, a large body of studies on the influence maximization problem has been conducted. Several influence spreading models and corresponding optimization algorithms have been proposed and successfully identified the infusive seeds in single isolated networks. However, as indicated by some recent studies and online materials, modern networked systems tend to have more complicated structures and multiple layers, which makes it difficult for existing seed determination techniques to deal with these networks. Thus, finding influential nodes in realistic multiplex networks remains open. Therefore, this paper aims to design an extended influence spreading model to simulate the influence diffusion process in multiplex networks, based on which a memetic algorithm is developed to find the seeds that are influential in all network layers. Experimental results on synthetic and real-world networks validate the effectiveness of the proposed algorithm. These results are helpful for identifying potential propagators in multiplex social networks, and provide solutions to analyze and gain deeper insights into networked systems.

Research on the Dynamic Multisocial Networks Influence Maximization Problem Based on Common Users

The influence maximization problem of a single social network is to find a set of $k$ seed nodes $S$ so that the spread of information from the seed set to the single network has the largest influence. This problem has attracted the attention of many researchers worldwide. In recent years, with the rapid development of the internet and the popularity of social networks, a variety of social platforms have appeared, allowing people to have multiple social accounts simultaneously; that is, one person will participate in multiple social networks and spread information on the various social platforms simultaneously. Consequently, the problem of influence maximization has been extended from a single social network to multiple social networks. However, many studies are based on static networks, and the critical challenge is that social networks usually have dynamic characteristics. At present, there is almost no research on dynamic multiple social networks. Therefore, based on common users, this paper establishes a dynamic multisocial network communication model to study the dynamic multisocial network influence maximization problem (DMNIMP). In this model, multiple dynamic networks are merged into a dynamic network, in which the self-propagating edges of common users are added to the snapshots of each frame of the integrated network. Experimental analysis shows that the proposed model can not only accurately and vividly represent dynamic characteristics but also reflect the mutual influence of common users on multiple social networks. If common users are chosen as the nodes with greater influence in each network, the communication range of the integrated network is obviously larger than that of a single network, and the interaction of dynamic multisocial networks is more obvious.

Influence Circle Covering in Large-Scale Social Networks: A Shift Approach

Given a specific propagation speed $h$ in a social network $G(V, E)$ , an influence circle(IC) of a node $s$ in time $t$ is a node set of its influenced nodes, where the distance between $s$ and its expected influenced node $w$ is less than radius $r=ht$ . Different from the Influence Maximization(IM) problem which finds a set of $k$ initial seed nodes in a network so that the expected size of cascade is maximized, the aim of the proposed influence circle covering (ICCovering) problem in this work is to find a minimum number of seeds or ICs to cover the whole network. The general approach for this covering problem is greedy strategy, which iteratively selects a seed with the largest influence circle. However, the upper bound of greedy algorithms does not perform very well, and the value will increase further as the network scale expands. In this paper, we propose an $\alpha $ -approximation partitioning algorithm for large-scale social networks, where $\alpha $ is the maximum number of outer edges of Voronoi cells appeared in the partition. The algorithm divides the input graph into smaller cells so that each cell can be solved separately, and a feasible solution to the input object can be constructed by combining the solutions of the smaller cells. When solving the smaller cells, we adopt the linear programming method. In order to improve its effectiveness and efficiency, we also propose two optimization algorithms. Extensive experiments on real social networks confirm the superiorities and effectiveness of our solution.

Influence Maximization in Signed Networks by Enhancing the Negative Influence

With the advancement of science and technology, research on influence maximization in networks has become a hot spot. In social networks, there is not only a positive relationship among nodes but also a negative impact, and the negative impact often plays a greater role than the positive impact, as observed for shopping websites or online votes. This paper proposes a method based on an independent cascade model by emphasizing the negative impact in symbolic networks to solve the problem of influence maximization. First, an algorithm that is based on an independent path and that emphasizes negative influence is designed to obtain the probability among nodes. Based on the activation probability, an algorithm is proposed to identify nodes that could have the greatest impact on the influence increment from the seeds. Finally, the seed set is confirmed based on the influence in the corresponding symbol network. In the experiment performed on real-world network data, the result indicate that the proposed algorithm causes more substantial influence propagation than do other algorithms.

On the Fairness of Time-Critical Influence Maximization in Social Networks

Influence maximization has found applications in a wide range of real-world problems, for instance, viral marketing of products in an online social network, and information propagation of valuable information such as job vacancy advertisements and health-related information. While existing algorithmic techniques usually aim at maximizing the total number of people influenced, the population often comprises several socially salient groups, e.g., based on gender or race. As a result, these techniques could lead to disparity across different groups in receiving important information. Furthermore, in many of these applications, the spread of influence is time-critical, i.e., it is only beneficial to be influenced before a time deadline. As we show in this paper, the time-criticality of the information could further exacerbate the disparity of influence across groups. This disparity, introduced by algorithms aimed at maximizing total influence, could have far-reaching consequences, impacting people's prosperity and putting minority groups at a big disadvantage. In this work, we propose a notion of group fairness in time-critical influence maximization. We introduce surrogate objective functions to solve the influence maximization problem under fairness considerations. By exploiting the submodularity structure of our objectives, we provide computationally efficient algorithms with guarantees that are effective in enforcing fairness during the propagation process. We demonstrate the effectiveness of our approach through synthetic and real-world experiments.

Maximizing the Diversity of Exposure in a Social Network

Social-media platforms have created new ways for citizens to stay informed and participate in public debates. However, to enable a healthy environment for information sharing, social deliberation, and opinion formation, citizens need to be exposed to sufficiently diverse viewpoints that challenge their assumptions, instead of being trapped inside filter bubbles. In this paper, we take a step in this direction and propose a novel approach to maximize the diversity of exposure in a social network. We formulate the problem in the context of information propagation, as a task of recommending a small number of news articles to selected users. We propose a realistic setting where we take into account content and user leanings, and the probability of further sharing an article. This setting allows us to capture the balance between maximizing the spread of information and ensuring the exposure of users to diverse viewpoints. The resulting problem can be cast as maximizing a monotone and submodular function subject to a matroid constraint on the allocation of articles to users. It is a challenging generalization of the influence maximization problem. Yet, we are able to devise scalable approximation algorithms by introducing a novel extension to the notion of random reverse-reachable sets. We experimentally demonstrate the efficiency and scalability of our algorithm on several real-world datasets.

An MCDM integrated adaptive simulated annealing approach for influence maximization in social networks

The Influence Maximization (IM) problem aims to identify a small subset of nodes that have the most influence spread in a network. Although it is an NP-hard problem, the continuous increasing size of the social networks leads to a substantially higher computational complexity, and therefore, has motivated numerous researchers to explore better approaches. This paper proposes a multi-criteria decision making (MCDM) based meta-heuristic approach to solve the IM problem in social networks. An MCDM approach is utilized to select candidate nodes by eliminating less influential ones at the preliminary phase which decreases the computation cost. Thereafter, to find the optimal solution, a modified version of Simulated Annealing (SA) with an enhanced search strategy is proposed. The performance of this proposed approach is tested and verified by solving the IM problem on eight real-life social networks of different sizes and types and comparing the results with six benchmark algorithms. The experimental results indicate that the proposed algorithm has a better trade-off between the solution quality and computational run time than the other algorithms.

Matching influence maximization in social networks

Influence maximization (IM) is a widely studied problem in social networks, which aims at finding a seed set with limited size that can maximize the expected number of influenced users. However, existing studies haven't considered the matching relationship, which refers to such scenarios that influenced users seek matched partners among the influenced users, such as time matching with friends to watch movie, or matching for opposite sex in the blind date. In this paper, we investigate different matching scenarios and propose online-matching (offline-matching), in which the matching and influence propagation are simultaneous (asynchronous). For the matching result, we introduce two matched types ‘s-matched’, i.e., i→j and ‘d-matched’, i.e., i↔j. Then, we formulate the matching influence maximization (MM) problem to optimize a limited seed set that maximizes the expected number of matched users. We prove that the MM problem is NP-hard and the computation of the matching influence is #P-hard. Next, we analyze the submodularity of the matching influence. To address the problem, we propose efficient methods OPMM (SAMM) to solve the MM in online-matching (offline-matching) with (1−1/e−ϵ)-approximation (β(1−1/e−ϵ)-approximation) guarantee. Experiments on the real-world datasets show our algorithms outperform state of the art algorithms in terms of more accurate matching propagation results.

Efficient diversified influence maximization with adaptive policies

Influence maximization (IM) in social media aims at finding influential seed users to trigger large online cascading influence spread. Existing studies mainly focus on maximizing the number of the activated nodes, but the diversity of the activated nodes has been mostly ignored even though it is crucial in many real-world applications, e.g., diversity of the influenced crowd can reduce the risk of marketing campaigns, or diversity of recommended items can improve the recommendation quality. In this paper, we study the diversified influence maximization (DIM) problem which aims to select k nodes such that both the number of activated nodes and the diversity of the activated nodes can be maximized. By designing a practical diversity function to model the distribution of activated nodes among all communities, we model the DIM problem by maximizing a parameterized linear combination of the diversity and the active node number. To tackle the NP-hardness of the DIM problem, we propose an efficient diversified influence maximization algorithm, diversified influence maximization via martingale (DIMM), which returns a 1−1∕e−ε-approximate solution with at least 1−2∕nℓ probability. Moreover, as the influence spread is highly stochastic and the DIM setting leaves no reserved measures for handling unforeseen events, we present an improved version of the algorithm named adaptive diversified influence maximization via martingale (ADIMM) with the adaptive setting. With the adaptive RI-πα policy, ADIMM is able to return an α(1−e−1∕α)-approximate solution with at least 1−1∕nℓ probability. Finally, we experimentally evaluate our algorithm against existing algorithms on large-scale real-world datasets. The experimental results validate the effectiveness and efficiency of our proposed algorithms.

A dynamic algorithm based on cohesive entropy for influence maximization in social networks

The problem of influence maximization in social networks has been widely investigated, but most previous studies have usually ignored the dynamic nature of propagation and the effects of local aggregation factors on diffusion. This paper presents a Dynamic algorithm based on cohesive Entropy for Influence Maximization (DEIM), the goal of which is to find the most influential nodes in social networks. Firstly, the Community Overlap Propagation Algorithm based on Cohesive Entropy (CECOPA) is put forward for the discovery of overlapping communities in networks, and potential nodes in the gathering area are selected to construct the candidate seed set. Then, the Optional Dynamic influence Propagation algorithm (ODP) is designed based on narrowing down the selection range of seeds. It utilizes a variety of entropy calculations to obtain the cohesive power between neighboring nodes and then determines whether the node has the ability to become a propagable pioneer of another node; thus, information continues to diffuse effectively. Finally, via many times experiments on several data sets, it is confirmed that the proposed DEIM algorithm in this paper can successfully affect the ideal number of users in different scenarios.

A multi-objective linear threshold influence spread model solved by swarm intelligence-based methods

The influence maximization problem (IMP) is one of the most important topics in social network analysis. It consists of finding the smallest seed of users that maximizes the influence spread in a social network. The main influence spread models are the linear threshold model (LT-model) and the independent cascade model (IC-model). These models have mainly been treated by using the single-objective paradigm which covers just one perspective: maximize the influence spread starting by given seed size, or minimize the seed set to reach a given number of influenced nodes. Sometimes, this minimization problem has been called the least cost influence problem (LCI). In this work, we propose a new optimization model for both perspectives under conflict, through the LT-model, by applying a binary multi-objective approach. Swarm intelligence methods are implemented to solve our proposal on real networks. Results are promising and suggest that the new multi-objective solution proposed can be properly solved in harder instances.

Estimating user influence ranking in independent cascade model

Nowadays, hundreds of millions of people use social networks to express their opinions and communicate with their friends. It is of importance to model and estimate the user influence in social networks. Since most studies perform Monte Carlo simulation to evaluate the user influence in the independent cascade model, which leads to tremendous computational costs, we introduce a duplicate forwarding model to characterize the diffusion process in social networks, and analyze the user influences below and above the diffusion threshold theoretically. After getting the user influence ranking, we propose a Spearman-like correlation coefficient to measure the correlation between two rankings, and find the analysis results from the duplicate forwarding model achieve much better accuracy than the measurements degree, betweenness, k-core and PageRank in estimating the user influence ranking in the independent cascade model. This approach can provide insights in modeling and estimating the influences of social network users, and can be easily extended to estimate the influence ranking for different seed sets in the problem of influence maximization.

MLPR: Efficient influence maximization in linear threshold propagation model using linear programming

Influence maximization is an important research topic in social networks that has different applications such as analyzing spread of rumors, interest, adoption of innovations, and feed ranking. The goal is to select a limited size subset of vertices (called a seed-set) in a Social Graph, so that upon their activation, a maximum number of vertices of the graph become activated, due to the influence of the vertices on each other. The linear threshold model is one of two classic stochastic propagation models that describe the spread of influence in a network. We present a new approach called MLPR (matrix multiplication, linear programming, randomized rounding) with linear programming used as its core in order to solve the influence maximization problem in the linear threshold model. Experiments on four real data sets have shown the efficiency of the MLPR method in solving the influence maximization problem in the linear threshold model. The spread of the output seed-sets is as large as when the state-of-the-art algorithms are used; however, unlike most of the existing algorithms, the runtime of our method is independent of the seed size and does not increase with it.

Influence maximization algorithm based on reducing search space in the social networks

The influence maximization problem in social networks is an optimization problem in viral marketing. This problem is concerned with identifying a certain number of people with the most influence in the social network level. Considering the NP-hard of this problem, finding an optimal solution with acceptable accuracy and the low running time is of the high importance. To this purpose, GIN (Group of Influential Nodes) algorithm is presented in this article which creates different groups of graph nodes with more connections than other groups. Then, it selects specific nodes from each group to reduce the search space to find the most influential nodes. Following the greedy method, it selects the seed nodes with the highest expected diffusion value. Experimental results show that the GIN algorithm has provided high influence spread along with low running time in comparison algorithms on all seven real-world datasets.

Influence maximization in the presence of vulnerable nodes: A ratio perspective

Influence maximization is a key problem seeking to identify users who will diffuse information to influence the largest number of other users in a social network. A drawback of the influence maximization problem is that it could be socially irresponsible to influence users many of whom would be harmed, due to their demographics, health conditions, or socioeconomic characteristics (e.g., predominantly overweight people influenced to buy junk food). Motivated by this drawback and by the fact that some of these vulnerable users will be influenced inadvertently, we introduce the problem of finding a set of users (seeds) that limits the influence to vulnerable users while maximizing the influence to the non-vulnerable users. We define a measure that captures the quality of a set of seeds as an additively smoothed ratio (ASR) between the expected number of influenced non-vulnerable users and the expected number of influenced vulnerable users. Then, we develop methods which aim to find a set of seeds that maximizes the measure: greedy heuristics, an approximation algorithm, as well as several variations of the approximation algorithm. We evaluate our methods on synthetic and real-world datasets and demonstrate they substantially outperform a state-of-the-art competitor in terms of both effectiveness and efficiency. We also demonstrate that the variations of our approximation algorithm offer different trade-offs between effectiveness and efficiency.

Competitive and complementary influence maximization in social network: A follower’s perspective

The problem of influence maximization is to select a small set of seed users in a social network to maximize the spread of influence. Recently, this problem has attracted considerable attention due to its applications in both commercial and social fields, such as product promotion, contagion prevention and public opinion forecasting. Most of prior work focuses on the diffusion model of single propagating entity, purely-complementary entities or purely-competitive entities. However, in reality, the influence diffusion in the social network is certainly more general, involving multiple propagating entities, which are competitive or complementary rather than single entity, purely-complementary entities or purely-competitive entities.In this paper, we consider the problem that a company (follower) intends to promote a new product into the market by maximizing the influence of a social network, where multiple competitive and complementary products have been spreading. We propose a Competitive and Complementary Independent Cascade (CCIC) diffusion model, and propose a novel optimization problem, follower-based influence maximization that aims to select top-K influential nodes as seed nodes, which can maximize the influence of a social network where multiple competitive and complementary products have already been propagated. To solve follower-based influence maximization problem, we propose a Deep Recursive Hybrid model (DRH) and an approximation algorithm (DRHGA). The DRH model dynamically tracks entity correlations, cascade correlations, causalities between ratings and next-period adoption through a deep recursive network and computes influence probabilities between nodes on target product. Then, with the influence probabilities predicted through DRH model, the DRHGA algorithm can efficiently find the seed node set for the target product under the CCIC diffusion model. Experimental results conducted on several public datasets show that our method outperforms the state-of-the-art methods on prediction accuracy and efficiency.

Influence Maximization on Undirected Graphs

We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ > 0) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model, the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem on both the linear threshold model and the weighted independent cascade model on undirected graphs that, in practice, find seed sets that on average obtain 97.52% of the performance of the much slower greedy algorithm for the linear threshold model and 97.39% of the performance of the greedy algorithm for the weighted independent cascade model. Our heuristics also outperform other popular local heuristics, such as the degree discount heuristic by Chen et al. [7].