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Graph convolutional neural networks (GCNNs) are popular deep learningarchitectures that, upon replacing regular convolutions with graph filters(GFs), generalize CNNs to irregular domains. However, classical GFs are proneto numerical errors since they consist of high-order polynomials. This problemis aggravated when several filters are applied in cascade, limiting thepractical depth of GCNNs. To tackle this issue, we present the neighborhoodgraph filters (NGFs), a family of GFs that replaces the powers of the graphshift operator with $k$-hop neighborhood adjacency matrices. NGFs help toalleviate the numerical issues of traditional GFs, allow for the design ofdeeper GCNNs, and enhance the robustness to errors in the topology of thegraph. To illustrate the advantage over traditional GFs in practicalapplications, we use NGFs in the design of deep neighborhood GCNNs to solvegraph signal denoising and node classification problems over both synthetic andreal-world data.

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