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

arXiv: https://arxiv.org/abs/2110.00844 · HTML: https://mlsanity.com/paper/2110.00844/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 2 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Dynamic Graph Message Passing Networks](https://mlsanity.com/paper/1908.06955/) (2019)
- [Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation](https://mlsanity.com/paper/2009.10812/) (2020)
- [Advances in Distributed Graph Filtering](https://mlsanity.com/paper/1808.03004/) (2018)
- [Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes](https://mlsanity.com/paper/2007.03266/) (2020)
- [Stability and Continuity of Centrality Measures in Weighted Graphs](https://mlsanity.com/paper/1410.5119/) (2014)
- [Deep Demixing: Reconstructing the Evolution of Epidemics Using Graph Neural Networks](https://mlsanity.com/paper/2011.09583/) (2020)
- [Robust graph-filter identification with graph denoising regularization](https://mlsanity.com/paper/2103.05976/) (2021)
- [An Underparametrized Deep Decoder Architecture for Graph Signals](https://mlsanity.com/paper/1908.00878/) (2019)

## Built on by (most cited first, 3 of 3)

- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)
- [Robust Graph Neural Network based on Graph Denoising](https://mlsanity.com/paper/2312.06557/) (2023)

## Abstract (arXiv)

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.