A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters
This work addresses a specific bottleneck in graph neural networks for researchers and practitioners, offering an incremental improvement over existing methods.
The paper tackled the problem of numerical errors in graph convolutional neural networks (GCNNs) caused by high-order polynomials in traditional graph filters, which limit network depth, by introducing neighborhood graph filters (NGFs) that replace these with k-hop neighborhood matrices, resulting in deeper GCNNs with improved robustness to topological errors and demonstrated advantages in graph signal denoising and node classification tasks.
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.