Peixoto Tiago P
Institut für Theoretische Physik, Universität Bremen, Hochschulring 18, D-28359 Bremen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042807. doi: 10.1103/PhysRevE.92.042807. Epub 2015 Oct 9.
Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges, or as a time dependence of the network structure. Although they are crucial for a more comprehensive scientific understanding, these representations offer substantial challenges. Namely, it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects. Furthermore, the direct incorporation of these features invariably increases the effective dimension of the network description, and hence aggravates the problem of overfitting, i.e., the use of overly complex characterizations that mistake purely random fluctuations for actual structure. In this work, we propose a robust and principled method to tackle these problems, by constructing generative models of modular network structure, incorporating layered, attributed and time-varying properties, as well as a nonparametric Bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence. We show that the method is capable of revealing hidden structure in layered, edge-valued, and time-varying networks, and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified. We illustrate our approach on a variety of empirical systems, including a social network of physicians, the voting correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.
许多网络系统由相互依存但又截然不同的交互类型组成，孤立地看无法完全理解这些交互。这些不同类型的交互通常表示为层、边上的属性或网络结构的时间依赖性。尽管它们对于更全面的科学理解至关重要，但这些表示带来了重大挑战。也就是说，如何精确刻画网络系统相对于这些附加方面的大尺度或中尺度结构是一个开放问题。此外，直接纳入这些特征总是会增加网络描述的有效维度，从而加剧过拟合问题，即使用过于复杂的刻画方式，将纯粹的随机波动误判为实际结构。在这项工作中，我们提出了一种稳健且有原则的方法来解决这些问题，即构建模块化网络结构的生成模型，纳入分层、属性和时变特性，以及一种非参数贝叶斯方法，用于从数据中推断参数并根据统计证据选择最合适的模型。我们表明该方法能够揭示分层、边值和时变网络中的隐藏结构，并且能够可靠地识别相对于附加维度最合适的粒度级别。我们在各种实证系统上展示了我们的方法，包括一个医生社交网络、巴西国民议会代表的投票相关性、全球机场网络以及一个高中生亲近网络。
