论文标题
低通图信号处理及其应用的用户指南
A User Guide to Low-Pass Graph Signal Processing and its Applications
论文作者
论文摘要
图形过滤器的概念可用于定义图形数据的生成模型。实际上，从许多网络动力学示例获得的数据可能被视为图形滤波器的输出。通过这种解释，已成功地应用了经典信号处理工具，例如频率分析，并与图形数据相似，从而为数据科学生成了新的见解。接下来是特定类图数据类别的用户指南，其中生成图滤波器是低通的，即，滤波器在较高的图形频率中减弱了内容，同时在较低的频率中保留了内容。我们的选择是由于应用领域（例如社交网络，金融市场和电力系统）中低通模型的普遍性所激发。我们说明了如何利用低通图滤波器的属性来学习图形拓扑或确定其社区结构；通过采样，恢复缺失的测量和DE-NOISE图数据有效地表示图形数据；低通属性还用作检测异常的基线。
The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal processing tools such as frequency analysis have been successfully applied with analogous interpretation to graph data, generating new insights for data science. What follows is a user guide on a specific class of graph data, where the generating graph filters are low-pass, i.e., the filter attenuates contents in the higher graph frequencies while retaining contents in the lower frequencies. Our choice is motivated by the prevalence of low-pass models in application domains such as social networks, financial markets, and power systems. We illustrate how to leverage properties of low-pass graph filters to learn the graph topology or identify its community structure; efficiently represent graph data through sampling, recover missing measurements, and de-noise graph data; the low-pass property is also used as the baseline to detect anomalies.
