Finding influential users for different time bounds in social networks using multi-objective optimization

Online social networks play an important role in marketing services. Influence maximization is a major challenge, in which the goal is to find the most influential users in a social network. Increasing the number of influenced users at the end of a diffusion process while decreasing the time of diffusion are two main objectives of the influence maximization problem. The goal of this paper is to find multiple sets of influential users such that each of them is the best set to spread influence for a specific time bound. Considering two conflicting objectives, increasing influence and decreasing diffusion time, we employ the NSGA-II algorithm which is a powerful algorithm in multi-objective optimization to find different seed sets with high influence at different diffusion times. Since social networks are large, computing influence and diffusion time of all chromosomes in each iteration will be challenging and computationally expensive. Therefore, we propose two methods which can estimate the expected influence and diffusion time of a seed set in an efficient manner. Providing the set of all potentially optimal solutions helps a decision maker evaluate the trade-offs between the two objectives, i.e., the number of influenced users and diffusion time. In addition, we develop an approach for selecting seed sets, which have optimal influence for specific time bounds, from the resulting Pareto front of the NSGA-II. Finally, we show that applying our algorithm to real social networks outperforms existing algorithms for the influence maximization problem. The results show a good compromise between the two objectives and the final seed sets result in high influence for different time bounds

Influence Maximization in Social Networks: A Survey

Online social networks have become an important platform for people to communicate, share knowledge and disseminate information. Given the widespread usage of social media, individuals' ideas, preferences and behavior are often influenced by their peers or friends in the social networks that they participate in. Since the last decade, influence maximization (IM) problem has been extensively adopted to model the diffusion of innovations and ideas. The purpose of IM is to select a set of k seed nodes who can influence the most individuals in the network. In this survey, we present a systematical study over the researches and future directions with respect to IM problem. We review the information diffusion models and analyze a variety of algorithms for the classic IM algorithms. We propose a taxonomy for potential readers to understand the key techniques and challenges. We also organize the milestone works in time order such that the readers of this survey can experience the research roadmap in this field. Moreover, we also categorize other application-oriented IM studies and correspondingly study each of them. What's more, we list a series of open questions as the future directions for IM-related researches, where a potential reader of this survey can easily observe what should be done next in this field

Influence-oriented community analysis in social networks

The emergence of online social networks has fundamentally changed the way people communicate with each other. Scholars have never ceased devoting their time and energy to the phenomenon since its emergence. Among researches around the social network, One line of study that draws a significant amount of attention recently is the discovery of communities, i.e., relatively densely connected sub-networks. Discovering such structures or communities provides insight into the relationship between individuals and composition of a social network. However, these studies mainly focus on the inner connection between individuals inside a community structure and neglect the external influence of a community as a whole. Another line of study in the field of the social network is influence analysis which analyze the ability of individuals to convince other users to adopt a new product (or an innovative idea, a service, a political opinion, etc.) with word-of-mouth effect which propagates information through network structures that can trigger cascades of further adoptions. However, these studies mainly focus on the relationship between individuals and the information diffusion process and neglect the community structures in a social network. There is a lack of studies that analyze the social influence of communities, which is fundamentally important for understanding the relationship between network structures and the information diffusion among it and has many practical applications. For example, a company may try to find the most influential community to advertise their products; an organization may intend to initiate a campaign in hope to attract more diverse customers, i.e., maximizing the number of influenced communities instead of customers; an association may hope to minimize the influence of a malicious information spread by one of its opponents, so that the community consisted of its core customers would be affected the least. To fill in this meaningful blank, in this thesis, we intend to analyze communities on the aspect of social influence and solve three research questions as follows. First, how to identify the communities with the dense intra-connections and the highest outer influence on the users outside the communities? Second, how to maximize both the spread and the diversity of the diffusion at the end of the information propagation by selecting a fixed number of influential users from a social network to spread the information. The higher diversity means more communities are influenced. Third, how to minimize the influence of a set of initial active nodes, which has been infected by a piece of malicious information, over a target community? The aim is to protect from this disinformation, by deleting a fixed number of edges in a social network. To address the first research question, we propose a new metric to measure the likelihood of the community to attract the other users outside the community within the social network, i.e., the community's outer influence. There are lots of applications that need to rank the communities using their outer influence, e.g., Ads trending analytics, social opinion mining and news propagation pattern discovery by monitoring the influential communities. We refer to such problem as Most Influential Community Search. While the most influential community search problem in large social networks is essential in various applications, it is mostly ignored by the academic research community. In this work, we systematically investigate this problem. Firstly, we propose a new community model, maximal kr-Clique community, which has desirable characters, i.e., society, cohesiveness, connectivity, and maximum. And then, we developed a novel tree-based index structure, denoted as C-Tree, to maintain the offline computed r-cliques. To efficiently search the most influential maximal kr-clique communities with the maximum outer influence, we developed four advanced index-based algorithms, which can improve the search performance of non-indexed solution by about 200 times. The efficiency and effectiveness of constructing index structure and evaluating the search algorithms have been verified using six real datasets including Facebook, Google+, Gowalla, Twitter, Youtube, and Amazon. A small case study shows the value of the most influential communities using DBLP data. To solve the second research question, we investigate Diverse Influence Maximization (DIM) to efficiently find k nodes which, at the end of propagation process, can maximize the number of activated nodes and the diversity of the activated nodes. In this work, an evaluation metric has been proposed to balance the two objectives. To address the computational challenges, we develop two efficient algorithms and one advanced PSP-Tree index. The effectiveness and efficiency of our DIM solution are verified by the extensive experimental studies on five real-world social network datasets. To address the last research question, we study the community-targeted influence minimization problem. Unlike previous influence minimization work, this study considers the influence minimization concerning a particular group of social network users, called targeted influence minimization. Thus, the objective is to protect a set of users, called target nodes, from malicious information originating from another group of users, called active nodes. This study also addresses two fundamental, but largely ignored, issues in different influence minimization problems: (i) the impact of a budget on the solution; (ii) robust sampling. To this end, two scenarios are investigated, namely unconstrained and constrained budget. Given an unconstrained budget, we provide an optimal solution; Given a constrained budget, we show the problem is NP-hard and develop a greedy algorithm with an (1 − 1/e)-approximation. More importantly, to solve the influence minimization problem in large, real-world social networks, we propose a robust sampling-based solution with a desirable theoretic bound. Extensive experiments using real social network datasets offer insight into the effectiveness and efficiency of the proposed solutions