arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1709.09002physics.soc-phcs.LGcs.SIphysics.data-an
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网络中有效排序的物理模型

A physical model for efficient ranking in networks

Columbia University(哥伦比亚大学);Santa Fe Institute(圣塔菲研究所);University of Colorado(科罗拉多大学)

Caterina De Bacco, Daniel B. Larremore, Cristopher Moore

摘要:

我们提出了一个物理启发的模型和一个有效的算法来推断有向网络中节点的层次排序。它将实值秩分配给节点,而不是简单的序数秩,并且它形式化了这样一个假设,即具有相似秩的个体之间更有可能发生交互。它为推断的层次结构提供了自然的统计显著性测试,并且可以用于执行推断任务,例如预测边的存在或方向。排名是通过求解线性方程组获得的,如果网络是稀疏的,则该线性方程组是稀疏的;因此所产生的算法是非常有效和可扩展的。我们通过分析真实和合成数据来说明这些发现,包括来自动物行为,教师招聘,社会支持网络和体育比赛的数据集。我们表明,我们的方法往往优于各种其他人,在速度和准确性,在恢复底层的排名和预测边缘方向。

英文摘要:

We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including datasets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions.

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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