局部谱图滤波器框架：统一框架、设计考虑综述和数值比较（扩展切割）
Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)
摘要：
将驻留在图上的数据表示为构建块信号的线性组合可以实现对数据的有效且有洞察力的视觉或统计分析，并且这种表示证明在信号处理和机器学习任务中作为正则化器是有用的。设计构建块信号的集合-或者更正式地说，原子字典-专门说明底层图结构以及任何可用的代表性训练信号一直是过去十年的一个活跃研究领域。在这篇文章中，我们调查了一类特殊的字典，称为本地化谱图过滤器框架，其原子是通过将谱模式本地化到图的不同区域来创建的。在展示了这个类如何包含从谱图小波到图滤波器组的各种方法之后，我们专注于如何设计谱滤波器和如何选择图案局部化的中心顶点这两个主要问题。在整个过程中，我们强调计算效率高的方法，确保所产生的变换及其逆可以应用于驻留在大型稀疏图上的数据。我们演示了如何这类变换方法可以用于信号处理任务，如去噪和非线性逼近，并提供代码，供读者在新的应用领域中试验这些方法。
英文摘要：
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal processing and machine learning tasks. Designing collections of building block signals -- or more formally, dictionaries of atoms -- that specifically account for the underlying graph structure as well as any available representative training signals has been an active area of research over the last decade. In this article, we survey a particular class of dictionaries called localized spectral graph filter frames, whose atoms are created by localizing spectral patterns to different regions of the graph. After showing how this class encompasses a variety of approaches from spectral graph wavelets to graph filter banks, we focus on the two main questions of how to design the spectral filters and how to select the center vertices to which the patterns are localized. Throughout, we emphasize computationally efficient methods that ensure the resulting transforms and their inverses can be applied to data residing on large, sparse graphs. We demonstrate how this class of transform methods can be used in signal processing tasks such as denoising and non-linear approximation, and provide code for readers to experiment with these methods in new application domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
