摘要翻译：
本文研究了从节点观测值推断无向图的问题，节点观测值被建模为依赖于未知网络结构的局部扩散动力学所产生的非平稳图信号。利用所谓的图移位算子(GSO)，它是图的一种矩阵表示，我们首先从扩散信号的实现中识别移位矩阵的特征向量，然后通过对待恢复的图施加期望的性质来估计特征值。与从观测数据的协方差矩阵直接得到特征向量的平稳情况不同，这里我们首先需要估计未知扩散（图）滤波器--在GSO中保持所求特征基的多项式。为了实现这个初始的系统辨识步骤，我们利用不同的信息源对任意相关的输入信号驱动图上的扩散。我们首先探索了一种更简单的情况，其中观测、输入信息和未知图过滤器是线性相关的。然后，我们讨论了这种关系由矩阵二次方程组给出的情况，这种情况出现在只有输入的二阶统计量可用的实用场景中。当二次滤波器辨识问题归结为一个非凸的四阶多项式极小化时，我们讨论了可辨识性条件，提出了逼近解的算法，并分析了它们的性能。数值实验表明，所提出的拓扑推断算法在利用合成和真实世界信号恢复大脑、社会、金融和城市交通网络方面的有效性。
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英文标题：
《Identifying the Topology of Undirected Networks from Diffused
  Non-stationary Graph Signals》
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作者：
Rasoul Shafipour, Santiago Segarra, Antonio G. Marques, and Gonzalo
  Mateos
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最新提交年份：
2019
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Computer Science        计算机科学
二级分类：Social and Information Networks        社会和信息网络
分类描述：Covers the design, analysis, and modeling of social and information networks, including their applications for on-line information access, communication, and interaction, and their roles as datasets in the exploration of questions in these and other domains, including connections to the social and biological sciences. Analysis and modeling of such networks includes topics in ACM Subject classes F.2, G.2, G.3, H.2, and I.2; applications in computing include topics in H.3, H.4, and H.5; and applications at the interface of computing and other disciplines include topics in J.1--J.7. Papers on computer communication systems and network protocols (e.g. TCP/IP) are generally a closer fit to the Networking and Internet Architecture (cs.NI) category.
涵盖社会和信息网络的设计、分析和建模，包括它们在联机信息访问、通信和交互方面的应用，以及它们作为数据集在这些领域和其他领域的问题探索中的作用，包括与社会和生物科学的联系。这类网络的分析和建模包括ACM学科类F.2、G.2、G.3、H.2和I.2的主题；计算应用包括H.3、H.4和H.5中的主题；计算和其他学科接口的应用程序包括J.1-J.7中的主题。关于计算机通信系统和网络协议（例如TCP/IP）的论文通常更适合网络和因特网体系结构（CS.NI）类别。
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英文摘要：
  We address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the unknown network. Using the so-called graph-shift operator (GSO), which is a matrix representation of the graph, we first identify the eigenvectors of the shift matrix from realizations of the diffused signals, and then estimate the eigenvalues by imposing desirable properties on the graph to be recovered. Different from the stationary setting where the eigenvectors can be obtained directly from the covariance matrix of the observations, here we need to estimate first the unknown diffusion (graph) filter -- a polynomial in the GSO that preserves the sought eigenbasis. To carry out this initial system identification step, we exploit different sources of information on the arbitrarily-correlated input signal driving the diffusion on the graph. We first explore the simpler case where the observations, the input information, and the unknown graph filter are linearly related. We then address the case where the relation is given by a system of matrix quadratic equations, which arises in pragmatic scenarios where only the second-order statistics of the inputs are available. While such quadratic filter identification problem boils down to a non-convex fourth-order polynomial minimization, we discuss identifiability conditions, propose algorithms to approximate the solution and analyze their performance. Numerical tests illustrate the effectiveness of the proposed topology inference algorithms in recovering brain, social, financial and urban transportation networks using synthetic and real-world signals.
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PDF链接：
https://arxiv.org/pdf/1801.03862