Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.

翻译：图神经网络（GNN）已成为节点分类和图分类等任务的有力工具。然而，针对信号分类的研究相对较少，此类任务涉及大量定义在单一图顶点上的函数（称为信号）。这类任务需要设计不同于传统GNN任务的网络架构。事实上，传统GNN依赖于局部化低通滤波器，而目标信号可能呈现复杂的多频行为并展现长程相互作用。这促使我们提出BLIS-Net（双李普希兹散射网络），一种基于先前提出的几何散射变换的新型GNN。该网络既能捕获局部与全局信号结构，也能同时提取低频与高频信息。我们对原始几何散射架构进行了多项关键改进，并证明这些改进增强了网络捕获输入信号信息的能力。实验表明，基于交通流量和fMRI数据的合成及真实数据集上，BLIS-Net均展现出优越性能。