A Hierarchical Generative Embedding Model for Influence Maximization in Attributed Social Networks

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.

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

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

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.

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.

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

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.

Influence maximization is a fundamental research problem in social networks. Viral marketing, one of its applications, is to get a small number of users to adopt a product, which subsequently triggers a large cascade of further adoptions by utilizing “Word-of-Mouth” effect in social networks. Time plays an important role in the influence spread from one user to another and the time needed for a user to influence another varies. In this paper, we propose the time constrained influence maximization problem. We show that the problem is NP-hard, and prove the monotonicity and submodularity of the time constrained influence spread function. Based on this, we develop a greedy algorithm. To improve the algorithm scalability, we propose the concept of Influence Spreading Path in social networks and develop a set of new algorithms for the time constrained influence maximization problem. We further parallelize the algorithms for achieving more time savings. Additionally, we generalize the proposed algorithms for the conventional influence maximization problem without time constraints. All of the algorithms are evaluated over four public available datasets. The experimental results demonstrate the efficiency and effectiveness of the algorithms for both conventional influence maximization problem and its time constrained version.

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.

The problem of Influence Maximization (IM) on social networks proposed firstly by Kempe et al. (2003) has been researched and developed with many cases. However, the IM in limited time while unwanted users are restricted is still a new potential subject. In this paper, we conducted the research over model of information diffusion named Locally Bounded Diffusion and tested some useful heuristic algorithms. The results of the experiment on some real datasets of social networks show that the algorithm meta-heuristic generated better output than the others.

A new algorithm for positive influence maximization in signed networks

Influence maximization problem with applications to viral marketing has gained much attention. Underlying influence diffusion models affect influence maximizing nodes because they focus on difference aspect of influence diffusion. Nevertheless, existing diffusion models overlook two important aspects of real-world marketing - continuous trials and time restriction. This paper proposes a new realistic influence diffusion model called Continously activated and Time-restricted IC (CT-IC) model which generalizes the IC model by embedding the above two aspects. We first prove that CT-IC model satisfies two crucial properties - monotonicity and submodularity. We then provide an efficient method for calculating exact influence spread when a social network is restricted to a directed tree and a simple path. Finally, we propose a scalable algorithm for influence maximization under CT-IC model called CT-IPA. Our experiments show that CT-IC model provides seeds of higher influence spread than IC model and CT-IPA is four orders of magnitude faster than the greedy algorithm while providing similar influence spread to the greedy algorithm.

Influence maximization problem focuses on finding a certain number of influential people to make their influence maximized in social networks. As positive influence has more practical significance in the viral marketing, we propose Positive Influence Maximization (PIM) problem and apply it in signed social networks. Considering the attitude of users to products, we propose a new propagation model named Linear Threshold model with Attitude (LT-A). In the model, each node has a new parameter η which denotes the attitude of node, and each edge has a new parameter ρ which denotes the relationships between nodes. We prove the PIM problem is NP-hard and the influence spread function is monotonous and submodular. Therefore, we use a greedy algorithm to obtain a solution with an approximation ratio of (1 − 1/e). Extensive experiments are conducted on two real-world network datasets and experimental results show that we can achieve higher influence spread than other existing approaches by using our model.

Starting with the earliest studies showing that the spread of new trends, information, and innovations is closely related to the social influence exerted on people by their social networks, the research on social influence theory took off, providing remarkable evidence on social influence induced viral phenomena. Fueled by the extreme popularity of online social networks and social media, computational social influence has emerged as a subfield of data mining whose goal is to analyze and optimize social influence using computational frameworks such as algorithm design and theoretical modeling. One of the fundamental problems in this field is the problem of influence maximization, primarily motivated by the application of viral marketing. The objective is to identify a small set of users in a social network who, when convinced to adopt a product, shall influence others in the network in a manner that leads to a large number of adoptions. In this tutorial, we extensively survey the research on social influence propagation and maximization, with a focus on the recent algorithmic and theoretical advances. To this end, we provide detailed reviews of the latest research effort devoted to (i) improving the efficiency and scalability of the influence maximization algorithms; (ii) context-aware modeling of the influence maximization problem to better capture real-world marketing scenarios; (iii) modeling and learning of real-world social influence; (iv) bridging the gap between social advertising and viral marketing.

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.