# A Simple Yet Effective SVD-GCN for Directed Graphs

arXiv: https://arxiv.org/abs/2205.09335 · HTML: https://mlsanity.com/paper/2205.09335/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Spectral Graph Attention Network with Fast Eigen-approximation](https://mlsanity.com/paper/2003.07450/) (2020)
- [Fast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity](https://mlsanity.com/paper/1705.07112/) (2017)

## Built on by (most cited first, 7 of 7)

- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond](https://mlsanity.com/paper/2309.02769/) (2023)
- [A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs](https://mlsanity.com/paper/2210.10993/) (2022)
- [Graph Convolutions Enrich the Self-Attention in Transformers!](https://mlsanity.com/paper/2312.04234/) (2023)
- [Generalized energy and gradient flow via graph framelets](https://mlsanity.com/paper/2210.04124/) (2022)
- [Revisiting Generalized p-Laplacian Regularized Framelet GCNs: Convergence, Energy Dynamic and Training with Non-Linear Diffusion](https://mlsanity.com/paper/2305.15639/) (2023)
- [Generalized Laplacian Regularized Framelet Graph Neural Networks](https://mlsanity.com/paper/2210.15092/) (2022)

## Abstract (arXiv)

In this paper, we propose a simple yet effective graph neural network for directed graphs (digraph) based on the classic Singular Value Decomposition (SVD), named SVD-GCN. The new graph neural network is built upon the graph SVD-framelet to better decompose graph signals on the SVD ``frequency'' bands. Further the new framelet SVD-GCN is also scaled up for larger scale graphs via using Chebyshev polynomial approximation. Through empirical experiments conducted on several node classification datasets, we have found that SVD-GCN has remarkable improvements in a variety of graph node learning tasks and it outperforms GCN and many other state-of-the-art graph neural networks for digraphs. Moreover, we empirically demonstate that the SVD-GCN has great denoising capability and robustness to high level graph data attacks. The theoretical and experimental results prove that the SVD-GCN is effective on a variant of graph datasets, meanwhile maintaining stable and even better performance than the state-of-the-arts.