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arXiv 2102.03569cs.SIcs.CY
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融合高阶交互的观点动力学

Opinion Dynamics Incorporating Higher-Order Interactions

Zuobai Zhang, Wanyue Xu, Zhongzhi Zhang, Guanrong Chen

AI总结:

针对现有观点动力学模型仅考虑最近邻交互的局限,提出融合高阶随机游走长程交互的新模型,证明其收敛性,并设计近线性复杂度的估计算法,经多社交网络实验验证兼具高效性与有效性。

摘要:

观点分享与形成问题已在学术文献中受到广泛关注,已有少量模型被提出用于研究该问题。然而,现有模型仅局限于最近邻之间的交互,忽略了二阶、三阶及更高阶邻居的交互,尽管高阶交互在真实社交网络中频繁出现。本文提出了一种基于高阶随机游走、融合长程交互的新型观点动力学模型。我们证明该模型会收敛到一个固定的观点向量,该向量可能与未考虑高阶交互的模型所得结果存在显著差异。由于直接计算均衡观点的计算成本极高,涉及大规模矩阵乘法和求逆运算,我们设计了一种具备理论收敛保证的估计算法,其在空间和时间上的复杂度相对于图中的边数近似呈线性。我们在多种社交网络上开展了大量实验,结果表明新算法兼具高效性和有效性。

英文摘要:

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, ignoring those second, third, and higher-order neighbors, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinion is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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