Analysis of Influence Maximization in Temporal Social Networks

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.

A key challenge in the social network community is the problem of network generation -- that is, how can we create synthetic networks that match characteristics traditionally found in most real world networks? Important characteristics that are present in social networks include a power law degree distribution, small diameter, and large amounts of clustering. However, most current network generators, such as the Chung Lu and Kronecker models, largely ignore the clustering present in a graph and focus on preserving other network statistics, such as the power law distribution. Models such as the exponential random graph model have a transitivity parameter that can capture clustering, but they are computationally difficult to learn, making scaling to large real world networks intractable. In this work, we propose an extension to the Chung Lu random graph model, the Transitive Chung Lu (TCL) model, which incorporates the notion transitive edges. Specifically, it combines the standard Chung Lu model with edges that are formed through transitive closure (e.g., by connecting a 'friend of a friend'). We prove TCL's expected degree distribution is equal to the degree distribution of the original input graph, while still providing the ability to capture the clustering in the network. The single parameter required by our model can be learned in seconds on graphs with millions of edges, networks can be generated in time that is linear in the number of edges. We demonstrate the performance of TCL on four real-world social networks, including an email dataset with hundreds of thousands of nodes and millions of edges, showing TCL generates graphs that match the degree distribution, clustering coefficients and hop plots of the original 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.

The analysis of social networks often assumes the time invariant scenario while in practice node attributes and links in such networks often evolve over time. In this paper, we propose a new method to predict node attributes and links in temporal networks.

Utilizing statistical physics and machine learning to discover collective behavior on temporal social networks

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

Background Online social networks share similar topological characteristics as real-world social networks. Many studies have been conducted to analyze the online social networks, but it is difficult to link human interests with social network software design. Purpose The goal of this work is to propose a methodology involving the analysis of human interactions for use in designing online social network software. Methods We propose a novel use of social network analysis techniques to elicit requirements in order to design better online Social network-based software. The validation case study involved the collection of real-world data by means of a questionnaire to perform a network design construction and analysis. The key idea is to examine social network to help in the identification of behaviors and interests of people for better software requirements elicitation. Results The validation case study demonstrates how unexpected centrality measures can emerge in real world networks. Our case study can thus conducted as a baseline for better requirement elicitation studies for online social network software design. This work also indicates how sociometric methods may be used to analyze any social domain as a possible standard practice in online social network software design. Overall, the study proved the effectiveness of the proposed novel methodology for the design of online social network software. The methodology specifically improves upon traditional methods for software design by involving social network modeling and analysis to first study the behavior and elicit requirements to develop more resilient online social network sites.

A discrete shuffled frog-leaping algorithm to identify influential nodes for influence maximization in social networks

Influence maximization (IM) aims to find a set of seed nodes in a social network that maximizes the influence spread. While most IM problems focus on classical influence cascades (e.g., Independent Cascade and Linear Threshold) which assume individual influence cascade probability is independent of the number of neighbors, recent studies by sociologists show that many influence cascades follow a pattern called complex contagion (CC), where influence cascade probability is much higher when more neighbors are influenced. Nonetheless, there are very limited studies on complex contagion influence maximization (CCIM) problems. This is partly because CC is non-submodular, the solution of which has been an open challenge. In this study, we propose the first reinforcement learning (RL) approach to CCIM. We find that a key obstacle in applying existing RL approaches to CCIM is the reward sparseness issue, which comes from two distinct sources. We then design a new RL algorithm that uses the CCIM problem structure to address the issue. Empirical results show that our approach achieves the state-of-the-art performance on four real-world networks.

A new algorithm for positive influence maximization in signed networks

Perhaps the most recent controversial topic in network science research is to determine whether real-world complex networks are scale-free or not. Recently, Broido and Clauset [A.D. Broido, A. Clauset, Nature Communication, 10, 1017 (2019)] asserted that the degree distributions of real-world networks are rarely power law under statistical tests. Such complex networks, including social, biological, information, temporal, and brain networks, are often heavy-tailed where the assumption on the scale-free nature of real-world heavy-tailed networks become insignificant as the complex system evolves over time. The failure of power law distribution in fitting the degree distribution data is mainly due to the presence of an identifiable non-linearity within the entire degree distribution in a log-log scale of a complex heavy-tailed network. In this study, we attempt to address this issue by proposing a new class of heavy-tailed probability distributions for modeling the entire degree distributions of complex networks. We introduce a new family of generalized Lomax models (GLM) to capture the non-linearity of these heavy-tailed networks. These newly introduced GLM-type distributions provide better fitting and greater flexibility to the entire node degree distribution of complex networks. Several statistical properties of the proposed model, such as extreme value and inferential statistical properties, are derived into this context. Interestingly, the GLM family belongs to the basin of attraction of Frechet distribution, a heavy-tailed extreme value distribution. Rigorous experimental analysis showcases the excellent performance of the proposed family of distributions while fitting the heavy-tailed real-world complex networks over fifty real-world datasets in comparison with benchmark probability models. Our results show that GLM-type distributions are not rare, able to model almost 90% of the tested networks accurately compared to benchmark probability models.

Influence maximization, aiming to select k seed users to influence the rest of users maximally, is a fundamental problem in social networks. Due to its well-known NP-hardness, great efforts have been devoted to developing scalable algorithms in the literature. However, the scalability issue is still not well solved in the time-sensitive influence maximization problem when propagation incurs a certain amount of time delay and only be valid before a deadline constraint, because all possible time delays need to be enumerated along each edge in a path to calculate the influence probability. Existing approaches usually adopt a path-based search strategy to enumerate all the possible influence spreading paths for a single path, which are computationally expensive for large social networks. In this paper, we propose a novel scalable time-sensitive influence maximization method, STIM, based on time-based search that can avoid a large number of repeated visits of the same subpaths and compute the influence probability more efficiently. Furthermore, based on time-based search, we also derive a new upper bound to estimate the marginal influence spread efficiently. Extensive experiments on real-world networks show that STIM is more space and time-efficient compared with existing state-of-the-art methods while still preserving the influence spread quality in real-world large social networks.

Healthcare social networking has known a prominent popularity. Nowadays, millions of healthcare communities are appeared. Community detection methods in social networks have essentially focused on static graphs neglecting the temporal characteristics of networks. Recently, motivated by the dynamic nature of real world projected on virtual social networks, an increasing number of evolutionary properties of communities issues are considered by research community. In this work, we aim to present a study on social networks across the time axis i.e. temporal social networks and we propose an algorithm classifying changes and based on indicators, and also we integrate data warehouse layer in order to have an over-view of all possible changes helpful for future analysis. The experimental results include an example of changes related to the apparition of diabetes in our country Tunisia.

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