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Scalable Influence Maximization in Social Networks under the Linear Threshold Model
"... Abstract—Influence maximization is the problem of finding a small set of most influential nodes in a social network so that their aggregated influence in the network is maximized. In this paper, we study influence maximization in the linear threshold model, one of the important models formalizing th ..."
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Cited by 72 (8 self)
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Abstract—Influence maximization is the problem of finding a small set of most influential nodes in a social network so that their aggregated influence in the network is maximized. In this paper, we study influence maximization in the linear threshold model, one of the important models formalizing the behavior of influence propagation in social networks. We first show that computing exact influence in general networks in the linear threshold model is #Phard, which closes an open problem left in the seminal work on influence maximization by Kempe, Kleinberg, and Tardos, 2003. As a contrast, we show that computing influence in directed acyclic graphs (DAGs) can be done in time linear to the size of the graphs. Based on the fast computation in DAGs, we propose the first scalable influence maximization algorithm tailored for the linear threshold model. We conduct extensive simulations to show that our algorithm is scalable to networks with millions of nodes and edges, is orders of magnitude faster than the greedy approximation algorithm proposed by Kempe et al. and its optimized versions, and performs consistently among the best algorithms while other heuristic algorithms not design specifically for the linear threshold model have unstable performances on different realworld networks. Keywordsinfluence maximization; social networks; linear threshold model; I.
A databased approach to social influence maximization
 PVLDB
"... Influence maximization is the problem of finding a set of users in a social network, such that by targeting this set, one maximizes the expected spread of influence in the network. Most of the literature on this topic has focused exclusively on the social graph, overlooking historical data, i.e., tr ..."
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Cited by 50 (11 self)
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Influence maximization is the problem of finding a set of users in a social network, such that by targeting this set, one maximizes the expected spread of influence in the network. Most of the literature on this topic has focused exclusively on the social graph, overlooking historical data, i.e., traces of past action propagations. In this paper, we study influence maximization from a novel databased perspective. In particular, we introduce a new model, which we call credit distribution, that directly leverages available propagation traces to learn how influence flows in the network and uses this to estimate expected influence spread. Our approach also learns the different levels of influenceability of users, and it is timeaware in the sense that it takes the temporal nature of influence into account. Weshowthatinfluencemaximizationunderthecreditdistribution model is NPhard and that the function that definesexpectedspreadunderourmodelissubmodular. Based on these, we develop an approximation algorithm for solving the influence maximization problem that at once enjoys high accuracy compared to the standard approach, while being several orders of magnitude faster and more scalable. 1.
What’s in a Hashtag? Content based Prediction of the Spread of Ideas in Microblogging Communities
"... Current social media research mainly focuses on temporal trends of the information flow and on the topology of the social graph that facilitates the propagation of information. In this paper we study the effect of the content of the idea on the information propagation. We present an efficient hybrid ..."
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Cited by 40 (1 self)
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Current social media research mainly focuses on temporal trends of the information flow and on the topology of the social graph that facilitates the propagation of information. In this paper we study the effect of the content of the idea on the information propagation. We present an efficient hybrid approach based on a linear regression for predicting the spread of an idea in a given time frame. We show that a combination of content features with temporal and topological features minimizes prediction error. Our algorithm is evaluated on Twitter hashtags extracted from a dataset of more than 400 million tweets. We analyze the contribution and the limitations of the various feature types to the spread of information, demonstrating that content aspects can be used as strong predictors thus should not be disregarded. We also study the dependencies between global features such as graph topology and content features.
CELF++: Optimizing the greedy algorithm for influence maximization in social networks
 In Proceedings of the 19th International World Wide Web Conference
, 2011
"... Kempe et al. [4] (KKT) showed the problem of influence maximization is NPhard and a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, it has two major sources of inefficiency. First, finding the expected spread of a node set is #Phard. Second, the basic g ..."
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Cited by 35 (2 self)
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Kempe et al. [4] (KKT) showed the problem of influence maximization is NPhard and a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, it has two major sources of inefficiency. First, finding the expected spread of a node set is #Phard. Second, the basic greedy algorithm is quadratic in the number of nodes. The first source is tackled by estimating the spread using Monte Carlo simulation or by using heuristics [4, 6, 2, 5, 1, 3]. Leskovec et al. [6] proposed the CELF algorithm for tackling the second. In this work, we propose CELF++ and empirically show that it is 3555 % faster than CELF.
Influence Maximization in Social Networks When Negative Opinions May Emerge and Propagate
"... Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that ..."
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Cited by 27 (6 self)
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Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 − 1/e. We define a quality sensitivity ratio (qsratio) of influence graphs and show a tight bound of Θ ( √ n/k) on the qsratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to compute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.
Sparsification of Influence Networks
"... We present Spine, an efficient algorithm for finding the “backbone ” of an influence network. Given a social graph and a log of past propagations, we build an instance of the independentcascade model that describes the propagations. We aim at reducing the complexity of that model, while preserving ..."
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Cited by 25 (6 self)
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We present Spine, an efficient algorithm for finding the “backbone ” of an influence network. Given a social graph and a log of past propagations, we build an instance of the independentcascade model that describes the propagations. We aim at reducing the complexity of that model, while preserving most of its accuracy in describing the data. We show that the problem is inapproximable and we presentanoptimal, dynamicprogrammingalgorithm,whose search space, albeit exponential, is typically much smaller than that of the brute force, exhaustivesearch approach. Seeking a practical, scalable approach to sparsification, we devise Spine, a greedy, efficient algorithm with practically little compromise in quality. We claim that sparsification is a fundamental datareduction operation with many applications, ranging from visualization to exploratory and descriptive data analysis. As a proof of concept, we use Spine on realworld datasets, revealing the backbone of their influencepropagation networks. Moreover, we apply Spine as a preprocessing step for the influencemaximization problem, showing that computations on sparsified models give up little accuracy, but yield significant improvements in terms of scalability.
Influence maximization in continuous time diffusion networks. arXiv preprint arXiv:1205.1682
, 2012
"... The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date ..."
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Cited by 23 (6 self)
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The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a network and its temporal dynamics, we first describe how continuous time Markov chains allow us to analytically compute the average total number of nodes reached by a diffusion process starting in a set of source nodes. We then show that selecting the set of most influential source nodes in the continuous time influence maximization problem is NPhard and develop an efficient approximation algorithm with provable nearoptimal performance. Experiments on synthetic and real diffusion networks show that our algorithm outperforms other state of the art algorithms by at least ∼20 % and is robust across different network topologies. 1.
Influence Blocking Maximization in Social Networks under the Competitive Linear Threshold Model
"... In many realworld 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) m ..."
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Cited by 23 (4 self)
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In many realworld 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 MonteCarlo 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 realworld 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.
Scalable influence estimation in continuoustime diffusion networks
 In
, 2013
"... If a piece of information is released from a media site, can we predict whether it may spread to one million web pages, in a month? This influence estimation problem is very challenging since both the timesensitive nature of the task and the requirement of scalability need to be addressed simultane ..."
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Cited by 21 (6 self)
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If a piece of information is released from a media site, can we predict whether it may spread to one million web pages, in a month? This influence estimation problem is very challenging since both the timesensitive nature of the task and the requirement of scalability need to be addressed simultaneously. In this paper, we propose a randomized algorithm for influence estimation in continuoustime diffusion networks. Our algorithm can estimate the influence of every node in a network with V  nodes and E  edges to an accuracy of using n = O(1/2) randomizations and up to logarithmic factorsO(nE+nV) computations. When used as a subroutine in a greedy influence maximization approach, our proposed algorithm is guaranteed to find a set of C nodes with the influence of at least (1 − 1/e) OPT−2C, where OPT is the optimal value. Experiments on both synthetic and realworld data show that the proposed algorithm can easily scale up to networks of millions of nodes while significantly improves over previous stateofthearts in terms of the accuracy of the estimated influence and the quality of the selected nodes in maximizing the influence. 1
Simpath: An efficient algorithm for influence maximization under the linear threshold model
 In Data Mining (ICDM), 2011 IEEE 11th International Conference on
, 2011
"... Abstract—There is significant current interest in the problem of influence maximization: given a directed social network with influence weights on edges and a number k, find k seed nodes such that activating them leads to the maximum expected number of activated nodes, according to a propagation mod ..."
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Cited by 19 (3 self)
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Abstract—There is significant current interest in the problem of influence maximization: given a directed social network with influence weights on edges and a number k, find k seed nodes such that activating them leads to the maximum expected number of activated nodes, according to a propagation model. Kempe et al. [1] showed, among other things, that under the Linear Threshold model, the problem is NPhard, and that a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, this algorithm suffers from various major performance drawbacks. In this paper, we propose SIMPATH, an efficient and effective algorithm for influence maximization under the linear threshold model that addresses these drawbacks by incorporating several clever optimizations. Through a comprehensive performance study on four real data sets, we show that SIMPATH consistently outperforms the state of the art w.r.t. running time, memory consumption and the quality of the seed set chosen, measured in terms of expected influence spread achieved.