A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters

TL;DR

This paper introduces neighborhood graph filters (NGFs), a new type of graph filter that improves the numerical stability and robustness of deep graph convolutional neural networks, enabling better performance in graph signal denoising and node classification.

Contribution

We propose NGFs, replacing powers of the graph shift with k-hop adjacency matrices, to enable deeper, more robust GCNNs with reduced numerical errors.

Findings

NGFs improve numerical stability of GCNNs.

Deeper GCNNs with NGFs outperform traditional filters.

NGFs enhance robustness to graph topology errors.

Abstract

Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with $k$-hop neighborhood adjacency matrices. NGFs help to alleviate the numerical issues of traditional GFs, allow for the design of deeper GCNNs, and enhance the robustness to errors in the topology of the graph. To illustrate the advantage over traditional GFs in practical applications, we use NGFs in the design of deep neighborhood GCNNs to solve graph signal denoising and node classification problems over both synthetic and real-world data.