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Register a new userTracking Infection Diffusion in Social Networks: Filtering Algorithms and Threshold Bounds
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This paper deals with the statistical signal pro- cessing over graphs for tracking infection diffusion in social networks. Infection (or Information) diffusion is modeled using the Susceptible-Infected-Susceptible (SIS) model. Mean field approximation is employed to approximate the discrete valued infected degree distribution evolution by a deterministic ordinary differential equation for obtaining a generative model for the infection diffusion. The infected degree distribution is shown to follow polynomial dynamics and is estimated using an exact non- linear Bayesian filter. We compute posterior Cramer-Rao bounds to obtain the fundamental limits of the filter which depend on the structure of the network. Considering the time-varying nature of the real world networks, the relationship between the diffusion thresholds and the degree distribution is investigated using generative models for real world networks. In addition, we validate the efficacy of our method with the diffusion data from a real-world online social system, Twitter. We find that SIS model is a good fit for the information diffusion and the non-linear filter effectively tracks the information diffusion.
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We propose a stochastic model for the diffusion of topics entering a social network modeled by a Watts-Strogatz graph. Our model sets into play an implicit competition between these topics as they vie for the attention of users in the network. The dynamics of our model are based on notions taken from real-world OSNs like Twitter where users either adopt an exogenous topic or copy topics from their neighbors leading to endogenous propagation. When instantiated correctly, the model achieves a viral regime where a few topics garner unusually good response from the network, closely mimicking the behavior of real-world OSNs. Our main contribution is our description of how clusters of proximate users that have spoken on the topic merge to form a large giant component making a topic go viral. This demonstrates that it is not weak ties but actually strong ties that play a major part in virality. We further validate our model and our hypotheses about its behavior by comparing our simulation results with the results of a measurement study conducted on real data taken from Twitter.
Current social networks are of extremely large-scale generating tremendous information flows at every moment. How information diffuse over social networks has attracted much attention from both industry and academics. Most of the existing works on information diffusion analysis are based on machine learning methods focusing on social network structure analysis and empirical data mining. However, the dynamics of information diffusion, which are heavily influenced by network users decisions, actions and their socio-economic interactions, is generally ignored by most of existing works. In this paper, we propose an evolutionary game theoretic framework to model the dynamic information diffusion process in social networks. Specifically, we derive the information diffusion dynamics in complete networks, uniform degree and non-uniform degree networks, with the highlight of two special networks, ErdH{o}s-Renyi random network and the Barabasi-Albert scale-free network. We find that the dynamics of information diffusion over these three kinds of networks are scale-free and the same with each other when the network scale is sufficiently large. To verify our theoretical analysis, we perform simulations for the information diffusion over synthetic networks and real-world Facebook networks. Moreover, we also conduct experiment on Twitter hashtags dataset, which shows that the proposed game theoretic model can well fit and predict the information diffusion over real social networks.
In this big data era, more and more social activities are digitized thereby becoming traceable, and thus the studies of social networks attract increasing attention from academia. It is widely believed that social networks play important role in the process of information diffusion. However, the opposite question, i.e., how does information diffusion process rebuild social networks, has been largely ignored. In this paper, we propose a new framework for understanding this reversing effect. Specifically, we first introduce a novel information diffusion model on social networks, by considering two types of individuals, i.e., smart and normal individuals, and two kinds of messages, true and false messages. Since social networks consist of human individuals, who have self-learning ability, in such a way that the trust of an individual to one of its neighbors increases (or decreases) if this individual received a true (or false) message from that neighbor. Based on such a simple self-learning mechanism, we prove that a social network can indeed become smarter, in terms of better distinguishing the true message from the false one. Moreover, we observe the emergence of social stratification based on the new model, i.e., the true messages initially posted by an individual closer to the smart one can be forwarded by more others, which is enhanced by the self-learning mechanism. We also find the crossover advantage, i.e., interconnection between two chain networks can make the related individuals possessing higher social influences, i.e., their messages can be forwarded by relatively more others. We obtained these results theoretically and validated them by simulations, which help better understand the reciprocity between social networks and information diffusion.
In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the problem that one entity tries to block the influence propagation of its competing entity as much as possible by strategically selecting a number of seed nodes that could initiate its own influence propagation. We call this problem the influence blocking maximization (IBM) problem. We prove that the objective function of IBM in the CLT model is submodular, and thus a greedy algorithm could achieve 1-1/e approximation ratio. However, the greedy algorithm requires Monte-Carlo simulations of competitive influence propagation, which makes the algorithm not efficient. We design an efficient algorithm CLDAG, which utilizes the properties of the CLT model, to address this issue. We conduct extensive simulations of CLDAG, the greedy algorithm, and other baseline algorithms on real-world and synthetic datasets. Our results show that CLDAG is able to provide best accuracy in par with the greedy algorithm and often better than other algorithms, while it is two orders of magnitude faster than the greedy algorithm.
Influencing (and being influenced by) others indirectly through social networks is fundamental to all human societies. Whether this happens through the diffusion of rumors, viruses, opinions, or know-how, finding the source is of persistent interest to people and an algorithmic challenge of much current research interest. However, no study has considered the case of diffusion sources actively trying to avoid detection. By disregarding this assumption, we risk conflating intentional obfuscation from the fundamental limitations of source-finding algorithms. We close this gap by separating two mechanisms hiding diffusion sources-one stemming from the network topology itself and the other from strategic manipulation of the network. We find that identifying the source can be challenging even without foul play and, many times, it is easy to evade source-detection algorithms further. We show that hiding connections that were part of the viral cascade is far more effective than introducing fake individuals. Thus, efforts should focus on exposing concealed ties rather than planted fake entities, e.g., bots in social media; such exposure would drastically improve our chances of detecting the source of a social diffusion.
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