  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.
