Convolutional Neural Network Architectures for Signals Supported on Graphs

TL;DR

This paper introduces two novel graph neural network architectures, selection GNN and aggregation GNN, which generalize CNNs for processing signals on graphs, demonstrating superior performance in source localization, authorship attribution, and text classification tasks.

Contribution

The paper proposes two new GNN architectures that extend CNN principles to graph-structured data, including a multinode version for large-scale graphs, and shows their effectiveness in various applications.

Findings

Multinode aggregation GNNs outperform other architectures.

The architectures reduce to traditional CNNs on time signals.

Effective in source localization and text classification.

Abstract

Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best performing GNN architecture.