# Low-Rank Projections of GCNs Laplacian

arXiv: https://arxiv.org/abs/2106.07360 · HTML: https://mlsanity.com/paper/2106.07360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Convergence and Stability of Graph Convolutional Networks on Large Random Graphs](https://mlsanity.com/paper/2006.01868/) (2020)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Tackling Over-Smoothing for General Graph Convolutional Networks](https://mlsanity.com/paper/2008.09864/) (2020)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [Revisiting Over-smoothing in Deep GCNs](https://mlsanity.com/paper/2003.13663/) (2020)
- [Stochastic Blockmodels meet Graph Neural Networks](https://mlsanity.com/paper/1905.05738/) (2019)
- [LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain](https://mlsanity.com/paper/1607.03463/) (2016)
- [Fisher-Bures Adversary Graph Convolutional Networks](https://mlsanity.com/paper/1903.04154/) (2019)
- [Interferometric Graph Transform: a Deep Unsupervised Graph Representation](https://mlsanity.com/paper/2006.05722/) (2020)
- [Spectral Embedding of Graph Networks](https://mlsanity.com/paper/2009.14441/) (2020)

## Abstract (arXiv)

In this work, we study the behavior of standard models for community detection under spectral manipulations. Through various ablation experiments, we evaluate the impact of bandpass filtering on the performance of a GCN: we empirically show that most of the necessary and used information for nodes classification is contained in the low-frequency domain, and thus contrary to images, high frequencies are less crucial to community detection. In particular, it is sometimes possible to obtain accuracies at a state-of-the-art level with simple classifiers that rely only on a few low frequencies.