# Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approach

arXiv: https://arxiv.org/abs/2108.10751 · HTML: https://mlsanity.com/paper/2108.10751/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Graph Coarsening with Preserved Spectral Properties](https://mlsanity.com/paper/1802.04447/) (2018)
- [Understanding Convolutional Neural Networks with A Mathematical Model](https://mlsanity.com/paper/1609.04112/) (2016)
- [Approximating Spectral Clustering via Sampling: a Review](https://mlsanity.com/paper/1901.10204/) (2019)
- [Distance and Position Estimation in Visible Light Systems with RGB LEDs](https://mlsanity.com/paper/2106.00396/) (2021)

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

- [Convolutional Neural Networks Demystified: A Matched Filtering Perspective Based Tutorial](https://mlsanity.com/paper/2108.11663/) (2021)
- [VS-CAM: Vertex Semantic Class Activation Mapping to Interpret Vision Graph Neural Network](https://mlsanity.com/paper/2209.09104/) (2022)
- [GraphNNK -- Graph Classification and Interpretability](https://mlsanity.com/paper/2602.00753/) (2026)

## Abstract (arXiv)

Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we revisit the operation of GCNNs and show that their convolution layers effectively perform matched filtering of input data with the chosen patterns (features). This allows us to provide a unifying account of GCNNs through a matched filter perspective, whereby the nonlinear ReLU and max-pooling layers are also discussed within the matched filtering framework. This is followed by a step-by-step guide on information propagation and learning in GCNNs. It is also shown that standard CNNs and fully connected NNs can be obtained as a special case of GCNNs. A carefully chosen numerical example guides the reader through the various steps of GCNN operation and learning both visually and numerically.