基于线性阈值模型的社会影响力网络分析
New Insights from an Analysis of Social Influence Networks under the Linear Threshold Model
摘要：
本文基于线性阈值模型研究了社会网络中的影响力传播。我们推导出一个分析表达式，用于评估的预期大小的最终影响集为一个给定的初始集，使用激活的概率为社会网络中的每个节点。然后，我们提供了一个等效的解释的影响力传播，在马尔可夫链中的非循环路径概率通过反转的边缘在社会网络的影响力图。我们使用这样的非循环路径概率的一些属性，以提供一个替代的子模块的影响函数的证明。我们说明了有用的分析表达式估计最有影响力的集，在特殊情况下，如UILT（均匀影响线性阈值），USLT（均匀磁化率线性阈值）和节点度为基础的影响模型。我们证明了PageRank启发式算法在上述模型中可以证明是最优的或表现非常好，并在更一般的情况下探索其局限性。最后，基于从解析表达式获得的见解，我们提供了一个有效的算法，近似的贪心算法的影响力最大化问题。
英文摘要：
We study the spread of influence in a social network based on the Linear Threshold model. We derive an analytical expression for evaluating the expected size of the eventual influenced set for a given initial set, using the probability of activation for each node in the social network. We then provide an equivalent interpretation for the influence spread, in terms of acyclic path probabilities in the Markov chain obtained by reversing the edges in the social network influence graph. We use some properties of such acyclic path probabilities to provide an alternate proof for the submodularity of the influence function. We illustrate the usefulness of the analytical expression in estimating the most influential set, in special cases such as the UILT(Uniform Influence Linear Threshold), USLT(Uniform Susceptance Linear Threshold) and node-degree based influence models. We show that the PageRank heuristic is either provably optimal or performs very well in the above models, and explore its limitations in more general cases. Finally, based on the insights obtained from the analytical expressions, we provide an efficient algorithm which approximates the greedy algorithm for the influence maximization problem.
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