论文标题
局部光谱图滤镜框架：统一框架，设计注意事项的调查和数值比较（扩展切割）
Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)
论文作者
论文摘要
代表位于图上的数据作为构建块信号的线性组合可以实现对数据的有效且有见地的视觉或统计分析，并且此类表示被证明是在信号处理和机器学习任务中作为正则化的。在过去的十年中，设计构建块信号的集合（或更正式的原子词典），这些词典是基础图结构以及任何可用的代表性培训信号的专门说明。在本文中，我们调查了一类称为局部光谱图滤镜框架的特定词典，其原子是通过将光谱模式定位到图表的不同区域而创建的。在展示了该类别如何包含从光谱图小波到图形滤波器库的各种方法之后，我们重点介绍了如何设计光谱过滤器以及如何选择图案所定位的中心顶点的两个主要问题。在整个过程中，我们强调了在计算上有效的方法，以确保所得转换及其对面可以应用于位于大而稀疏图上的数据。我们演示了如何将此类别的转换方法用于信号处理任务，例如Denoising和非线性近似，并为读者提供代码，以在新的应用程序域中尝试这些方法。
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.
