论文标题
基于热半群的图形的散射变换，并应用了在正时序列中检测异常的情况
A scattering transform for graphs based on heat semigroups, with an application for the detection of anomalies in positive time series with underlying periodicities
论文作者
论文摘要
本文开发了Mallat散射转换的自适应版本，以用于图形上的信号。主要结果是转换层的规范界限，该层是从Beurling-deny不平等版本获得的，该版本允许删除散射转换中的非线性步骤。根据输入信号的统计假设，可以完善规范界限。此处提出的概念通过对交通计数的申请进行了说明，这些交通计数每天和每周都有特征性的周期性。偏离这些预期的周期性的异常交通模式在散射变换中产生响应。
This paper develops an adaptive version of Mallat's scattering transform for signals on graphs. The main results are norm bounds for the layers of the transform, obtained from a version of a Beurling-Deny inequality that permits to remove the nonlinear steps in the scattering transform. Under statistical assumptions on the input signal, the norm bounds can be refined. The concepts presented here are illustrated with an application to traffic counts which exhibit characteristic daily and weekly periodicities. Anomalous traffic patterns which deviate from these expected periodicities produce a response in the scattering transform.
