图散射变换的稳定性
Stability of Graph Scattering Transforms
摘要：
散射变换是不可训练的深度卷积架构，其利用小波滤波器组的多尺度分辨率来获得数据的适当表示。更重要的是，他们被证明是不变的翻译，并稳定的扰动接近翻译。这种稳定性使散射变换对数据度量域中的小变化具有鲁棒性。当考虑网络数据时，规则卷积不成立，因为数据域呈现由网络拓扑给出的不规则结构。在这项工作中，我们扩展了散射变换网络数据使用多分辨率图小波，其计算可以通过图卷积。此外，我们证明了由此产生的图散射变换是稳定的度量扰动的基础网络。这使得图散射变换对网络拓扑结构的变化具有鲁棒性，使其对于迁移学习、拓扑估计或时变图的情况特别有用。
英文摘要：
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stability property dons the scattering transform with a robustness to small changes in the metric domain of the data. When considering network data, regular convolutions do not hold since the data domain presents an irregular structure given by the network topology. In this work, we extend scattering transforms to network data by using multiresolution graph wavelets, whose computation can be obtained by means of graph convolutions. Furthermore, we prove that the resulting graph scattering transforms are stable to metric perturbations of the underlying network. This renders graph scattering transforms robust to changes on the network topology, making it particularly useful for cases of transfer learning, topology estimation or time-varying graphs.
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。
