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 and identify its community structure; efficiently represent graph data through sampling; recover missing measurements; and denoise graph data. The low-pass property is also used as the baseline to detect anomalies.

中文翻译：

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低通图形信号处理及其应用用户指南：工具和应用

图过滤器的概念可用于定义图数据的生成模型。事实上，从许多网络动态示例中获得的数据可以被视为图形过滤器的输出。通过这种解释，经典的信号处理工具，例如频率分析，已经成功地应用于图形数据的类似解释，为数据科学产生了新的见解。以下是特定类别图形数据的用户指南，其中生成的图形过滤器是低通的；即，滤波器衰减较高图频率中的内容，同时保留较低频率中的内容。我们的选择是由于低通模型在社交网络、金融市场和电力系统等应用领域的流行。我们说明了如何利用低通图过滤器的特性来学习图拓扑并识别其社区结构；通过采样有效地表示图形数据；恢复丢失的测量值；和去噪图数据。低通特性也被用作检测异常的基线。