A Learning Automaton-Based Algorithm 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

Efficient Influence Maximization in Social-Networks Under Independent Cascade Model

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.

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.

Influence maximization, defined as finding a small subset of nodes that maximizes spread of influence in social networks, is NP-hard under both Independent Cascade (IC) and Linear Threshold (LT) models, where many greedy-based algorithms have been proposed with the best approximation guarantee. However, existing greedy-based algorithms are inefficient on large networks, as it demands heavy Monte-Carlo simulations of the spread functions for each node at the initial step [7] . In this paper, we establish new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. We theoretically prove that the bound is tight and convergent when the summation of weights towards (or from) each node is less than 1. Based on the bound, we propose a new Upper Bound based Lazy Forward algorithm ( UBLF in short) for discovering the top-k influential nodes in social networks. We test and compare UBLF with prior greedy algorithms, especially CELF [30] . Experimental results show that UBLF reduces more than 95 percent Monte-Carlo simulations of CELF and achieves about $2\hbox{-}10$ times speedup when the seed set is small.

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

Influence maximization deals with the problem of identifying k-size subset of nodes in a social network that can maximize the influence spread in the network. In this paper, the problem of influence maximization using two aspects, node connectivity and node activity level, has been studied. To measure node connectivity, the widely popular and intuitive measure of out-degree of node has been used, and for node activity, node’s past interactions have been taken into consideration. For studying influence spread, two activity-based diffusion models, namely Activity-based Independent Cascade model and Activity-based Linear Threshold model, have been proposed in which influence propagation is driven by a node’s activity that it has actually performed in the past. Activity-based models aim at studying influence spread by incorporating a more realistic aspect corresponding to user behavior. Motivated by the belief that activity is as important as connectivity, UAC-Rank algorithm for the identification of initial adopters has been proposed.

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, an equivalence between the two models is established, except that the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem (the optimization problem of selecting a set of nodes as initial seeds in a social network to maximize their influence) with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model.

A new algorithm for positive influence maximization in signed networks

Influence Maximization (IM) is the problem of finding k most influential users in a social network. In this paper, a novel propagation model named Independent Cascade Model with Limited Propagation Distance (ICLPD) is established. In the ICLPD, the influence of seed nodes can only propagate limited hops and the transmission capacities of the seed nodes are different. It is proved that IM problem in the ICLPD is NP-hard and the influence spread function has submodularity. Thus a greedy algorithm can be used to get a result which guarantees a ratio of (1 − 1/e) approximation. In addition, an efficient heuristic algorithm named Local Influence Discount Heuristic (LIDH) is proposed to speed up the greedy algorithm. Extensive experiments on two real-world datasets show LIDH works well in the ICLPD. LIDH is several orders of magnitude faster than the greedy algorithm while its influence spread is close to that of the greedy algorithm.Keywordsinfluence maximizationpropagation modelslimited propagation distancelocal influenceheuristic algorithm

We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ>0$) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper-bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model called the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem on both the linear threshold model and the weighted independent cascade model on undirected graphs that, in practice, find seed sets which on average obtain 97.52% of the performance of the much slower greedy algorithm for the linear threshold model, and 97.39% of the performance of the greedy algorithm for the weighted independent cascade model. Our heuristics also outperform other popular local heuristics, such as the degree discount heuristic by Chen et al.

We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ > 0) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model, the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem on both the linear threshold model and the weighted independent cascade model on undirected graphs that, in practice, find seed sets that on average obtain 97.52% of the performance of the much slower greedy algorithm for the linear threshold model and 97.39% of the performance of the greedy algorithm for the weighted independent cascade model. Our heuristics also outperform other popular local heuristics, such as the degree discount heuristic by Chen et al. [7].

Influence maximization is to extract a small set of nodes from a social network which influences the propagation maximally under a cascade model. In this paper, we propose a memetic algorithm for community-based influence maximization in social networks. The proposed memetic algorithm optimizes the 2-hop influence spread to find the most influential nodes. Problem-specific population initialization and similarity-based local search are designed to accelerate the convergence of the algorithm. Experiments on three realworld datasets demonstrate that our algorithm has competitive performances to the comparing algorithms in terms of effectiveness and efficiency. For example, on a real-world network of 15233 nodes and 58891 edges, the influence spread of the proposed algorithm is 12.5%, 13.2% and 173.5% higher than the three comparing algorithms Degree, PageRank and Random, respectively.

We consider the influence maximization problem (selecting k seeds in a network maximizing the expected total influence) on undirected graphs under the linear threshold model. On the one hand, we prove that the greedy algorithm always achieves a (1−(1−1/k)^k+Ω(1/k^3))-approximation, showing that the greedy algorithm does slightly better on undirected graphs than the generic (1−(1−1/k)^k) bound which also applies to directed graphs. On the other hand, we show that substantial improvement on this bound is impossible by presenting an example where the greedy algorithm can obtain at most a (1−(1−1/k)^k+O(1/k^0.2)) approximation. This result stands in contrast to the previous work on the independent cascade model. Like the linear threshold model, the greedy algorithm obtains a (1−(1−1/k)^k)-approximation on directed graphs in the independent cascade model. However, Khanna and Lucier showed that, in undirected graphs, the greedy algorithm performs substantially better: a (1−(1−1/k)^k+c) approximation for constant c>0. Our results show that, surprisingly, no such improvement occurs in the linear threshold model. Finally, we show that, under the linear threshold model, the approximation ratio (1−(1−1/k)^k) is tight if 1) the graph is directed or 2) the vertices are weighted. In other words, under either of these two settings, the greedy algorithm cannot achieve a (1−(1−1/k)^k+f(k))-approximation for any positive function f(k). The result in setting 2) is again in a sharp contrast to Khanna and Lucier's (1−(1−1/k)^k+c)-approximation result for the independent cascade model, where the (1−(1−1/k)^k+c) approximation guarantee can be extended to the setting where vertices are weighted. We also discuss extensions to more generalized settings including those with edge-weighted graphs.

Influence maximization is an optimization problem that aims at finding a small set of nodes as seed nodes to maximize the spread of influence in a social network. In this paper, we introduce a new technique called Non-backtracking Random Walk into the influence maximization problem. An optimized algorithm, called NBRW, is devised through sampling nodes when applying restricted non-backtracking walk in network communities. Node's traversing number gives a good estimate of its influence. Our algorithm can be executed in linear time, which beats other influence maximization algorithms. We give extensive experiments under various diffusion models against other state-of-the-art node-selection algorithms. It demonstrates that in terms of influence range and convergent speed our algorithm gives a superior performance under most diffusion models, especially for linear threshold model.