Connecting the Dots
Connecting the Dots
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DOI：
10.1109/msp.2018.2890143
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发表时间：
2019-05-01
影响因子：
14.9
通讯作者：
Ribeiro, Alejandro
中科院分区：
文献类型：
--
作者：
Mateos, Gonzalo;Segarra, Santiago;Ribeiro, Alejandro
网络拓扑推理是网络科学中的一个重要问题。迄今为止，大多数图信号处理（GSP）工作都假设底层网络是已知的，然后分析图的代数和谱特征如何影响感兴趣的图信号的性质。这种假设通常是站不住脚的应用程序处理，例如，直接观察到的社会和基础设施网络；通常采用的图构造方案在很大程度上是非正式的，明显缺乏验证元素。本文概述了通过使用从图信号中获得的信息来推断底层图拓扑的图学习方法，以弥合上述差距。首先考察了相当成熟的统计方法，其中相关分析及其与协方差选择和高维回归的联系是学习高斯图模型的中心阶段。最近基于gsp的网络推理框架也被描述，它假设网络作为潜在的底层结构存在，并且观察结果是在这样一个图中定义的网络过程的结果。本文还简要概述了一些有争议的新兴主题，包括动态网络的推理和成对相互作用的非线性模型，以及对有向图（di）的扩展及其与因果推理的关系。总而言之，本文向读者介绍了SP研究在新兴主题领域的挑战和机遇，这些领域处于建模、预测和控制复杂行为的十字路口，这些行为出现在随着时间的推移而演变的网络系统中。
Network topology inference is a significant problem in network science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with, e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This article offers an overview of graph-learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks and nonlinear models of pairwise interaction, as well as extensions to directed (di) graphs and their relation to causal inference. All in all, this article introduces readers to challenges and opportunities for SP research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.