CAREER: Inferring Graph Structure via Spectral Representations of Network Processes

要应对网络科学和大数据交叉领域的挑战，就必须在分布式网络过程的建模、识别和可控性方面取得根本性突破--这些过程通常被概念化为图上定义的信号。在常规域（时间或空间）上定义的信号的科学理解与图值信号之间存在明显的不匹配。关于时间序列的知识是在几十年的时间里发展起来的，并受到通信、语音或控制等领域的真实的需求的推动。相反，与网络有关的信号处理问题的普遍存在和获得高质量网络数据是最近的事件。在这种情况下，该项目的研究旨在推动网络分析信息处理的知识前沿，从而在理解强耦合系统（如大脑）的内在复杂性方面取得进展。学生还将接受培训，以解决大数据和网络科学的交叉问题，从而有助于劳动力的发展。在假设信号与支持它们的图的拓扑结构相关的情况下，图信号处理的目标是开发有效利用这种关系结构的算法，并且可以在仅部分观察到这些关系时对它们进行推断。迄今为止，大多数图形信号处理工作都假设底层网络是已知的，然后分析图形的代数和频谱特性如何影响感兴趣的图形信号的属性。然而，这样的假设在实践中往往是站不住脚的，可以说大多数图构造方案在很大程度上是非正式的，明显缺乏验证的元素。 该研究项目的智力价值是研究如何使用从图形信号中获得的信息，通过在图形谱域中操作的创新方法来学习底层图形拓扑。我们的想法是考虑与任意图形相关联的快照信号的图形傅立叶变换，并且在所有可行的网络中，搜索一个赋予所得到的变换具有目标频谱特性和所寻求的图形具有吸引人的物理特性的网络。与当前数据驱动的复杂网络系统科学研究的趋势相一致，目标是从：（i）描述性帐户转向可以解释和预测网络行为的推理图形信号处理技术;以及从（ii）特设图构造到严格的公式，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Coping with the challenges found at the intersection of Network Science and Big Data necessitates fundamental breakthroughs in modeling, identification, and controllability of distributed network processes -- often conceptualized as signals defined on graphs. There is an evident mismatch between the scientific understanding of signals defined over regular domains (time or space) and graph-valued signals. Knowledge about time series was developed over the course of decades and boosted by real needs in areas such as communications, speech, or control. On the contrary, the prevalence of network-related signal processing problems and the access to quality network data are recent events. In this context, research in this project aims to push the frontiers of knowledge in network-analytic information processing, and thus make progress towards understanding the inherent complexities of strongly coupled systems such as the brain. Students will also be trained to tackle the problems at the intersection of Big Data and Network Science, thereby contributing to workforce development as well.Under the assumption that the signals are related to the topology of the graph where they are supported, the goal of graph signal processing is to develop algorithms that fruitfully leverage this relational structure, and can make inferences about these relationships when they are only partially observed. Most graph signal processing 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. However, such assumption is often untenable in practice and arguably most graph construction schemes are largely informal, distinctly lacking an element of validation. The intellectual merit of this research project is to investigate how to use information available from graph signals to learn the underlying graph topology, through innovative approaches that operate in the graph spectral domain. The idea is to consider the graph Fourier transform of the snapshot signals associated with an arbitrary graph and, among all the feasible networks, search for one that endows the resulting transforms with target spectral properties and the sought graph with appealing physical characteristics. Aligned with current trends in data-driven scientific inquiry into complex networked systems, the aim is to shift from: (i) descriptive accounts to inferential graph signal processing techniques that can explain as well as predict network behavior; and from (ii) ad hoc graph constructions to rigorous formulations rooted in well-defined models and principles.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.