Laplacian-Eigenvector基下网络舆论和传播状态的可压缩性
Compressibility of Network Opinion and Spread States in the Laplacian-Eigenvector Basis
摘要：
网络上的意见演变和传播过程（例如，传染病传播、社交网络中意见形成）不仅是高维的，而且在性质上是易变的和多尺度的。在本研究中，我们探讨这些过程的快照数据是否可以接受简洁的表示。具体而言，使用三个案例研究，我们探讨数据是否是可压缩的拉普拉斯特征向量的基础上，在这个意义上，每个快照可以很好地近似使用一个（可能不同的）小的一组基向量。第一个案例研究涉及的是一个线性共识模型，是在一个未知的位置随机输入，经验和正式的分析被用来表征压缩性。其次，通过实证研究评估了随机选民模型的状态快照的可压缩性。最后，研究了州级每日COVID-19阳性率数据的可压缩性。这三个案例研究表明，从意见演变和传播过程中的状态快照允许简洁的表示，但捕获其丰富的传播动态。
英文摘要：
Opinion-evolution and spread processes on networks (e.g., infectious disease spread, opinion formation in social networks) are not only high dimensional but also volatile and multiscale in nature. In this study, we explore whether snapshot data from these processes can admit terse representations. Specifically, using three case studies, we explore whether the data are compressible in the Laplacian-eigenvector basis, in the sense that each snapshot can be approximated well using a (possibly different) small set of basis vectors. The first case study is concerned with a linear consensus model that is subject to a stochastic input at an unknown location; both empirical and formal analyses are used to characterize compressibility. Second, compressibility of state snapshots for a stochastic voter model is assessed via an empirical study. Finally, compressibility is studied for state-level daily COVID-19 positivity-rate data. The three case studies indicate that state snapshots from opinion-evolution and spread processes allow terse representations, which nevertheless capture their rich propagative dynamics.
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