Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is subject to error or natural changes over time. This motivated a new perspective on GSP, where the signal processing framework is developed for an entire class of graphs with similar structures. This approach can be formalized via the theory of graph limits, where graphs are considered as random samples from a distribution represented by a graphon. When the network under consideration has underlying symmetries, they may be modeled as samples from Cayley graphons. In Cayley graphons, vertices are sampled from a group, and the link probability between two vertices is determined by a function of the two corresponding group elements. Infinite groups such as the 1-dimensional torus can be used to model networks with an underlying spatial reality. Cayley graphons on finite groups give rise to a Stochastic Block Model, where the link probabilities between blocks form a (edge-weighted) Cayley graph. This manuscript summarizes some work on graph signal processing on large networks, in particular samples of Cayley graphons.

翻译：当前图信号处理方法高度依赖底层网络的特定结构：移位算子和图傅里叶变换均直接基于具体图推导得出。许多情况下，网络会随时间的推移产生误差或自然变化。这促使图信号处理领域提出新视角——针对具有相似结构的整类图发展信号处理框架。该研究途径可通过图极限理论形式化，其中图被视为由图极限分布表示的随机样本。当所涉及网络存在底层对称性时，可将其建模为凯莱图极限的样本。在凯莱图极限中，顶点从群中采集，两顶点间的连接概率由对应群元素的函数决定。无限群（如一维环面）可用于建模具有底层空间现实性的网络。有限群上的凯莱图极限可生成随机块模型，其中块间连接概率构成（边加权）凯莱图。本文综述了大规模网络（尤其是凯莱图极限样本）上图信号处理的部分研究成果。