# How Powerful is Graph Convolution for Recommendation?

arXiv: https://arxiv.org/abs/2108.07567 · HTML: https://mlsanity.com/paper/2108.07567/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 17 Aug 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Neural Collaborative Filtering vs. Matrix Factorization Revisited](https://mlsanity.com/paper/2005.09683/) (2020)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction](https://mlsanity.com/paper/2105.10446/) (2021)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Optimization of Graph Neural Networks: Implicit Acceleration by Skip Connections and More Depth](https://mlsanity.com/paper/2105.04550/) (2021)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [Spectral Collaborative Filtering](https://mlsanity.com/paper/1808.10523/) (2018)
- [Graph Convolutional Network for Recommendation with Low-pass Collaborative Filters](https://mlsanity.com/paper/2006.15516/) (2020)
- [Collaborative Memory Network for Recommendation Systems](https://mlsanity.com/paper/1804.10862/) (2018)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [BiRank: Towards Ranking on Bipartite Graphs](https://mlsanity.com/paper/1708.04396/) (2017)
- [Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training](https://mlsanity.com/paper/2103.00673/) (2021)
- [Markov Random Fields for Collaborative Filtering](https://mlsanity.com/paper/1910.09645/) (2019)

## Built on by (most cited first, 30 of 50)

- [OpenGraph: Towards Open Graph Foundation Models](https://mlsanity.com/paper/2403.01121/) (2024)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [Towards Graph Contrastive Learning: A Survey and Beyond](https://mlsanity.com/paper/2405.11868/) (2024)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Collaborative Filtering Based on Diffusion Models: Unveiling the Potential of High-Order Connectivity](https://mlsanity.com/paper/2404.14240/) (2024)
- [GraphPro: Graph Pre-training and Prompt Learning for Recommendation](https://mlsanity.com/paper/2311.16716/) (2023)
- [OAG-Bench: A Human-Curated Benchmark for Academic Graph Mining](https://mlsanity.com/paper/2402.15810/) (2024)
- [ReFactor GNNs: Revisiting Factorisation-based Models from a Message-Passing Perspective](https://mlsanity.com/paper/2207.09980/) (2022)
- [Parameter-free Dynamic Graph Embedding for Link Prediction](https://mlsanity.com/paper/2210.08189/) (2022)
- [Triple Structural Information Modelling for Accurate, Explainable and Interactive Recommendation](https://mlsanity.com/paper/2304.11528/) (2023)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [RevGNN: Negative Sampling Enhanced Contrastive Graph Learning for Academic Reviewer Recommendation](https://mlsanity.com/paper/2407.20684/) (2024)
- [It's Enough: Relaxing Diagonal Constraints in Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2305.12922/) (2023)
- [Heterophily-Aware Fair Recommendation using Graph Convolutional Networks](https://mlsanity.com/paper/2402.03365/) (2024)
- [Turbo-CF: Matrix Decomposition-Free Graph Filtering for Fast Recommendation](https://mlsanity.com/paper/2404.14243/) (2024)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [Personality-Driven Social Multimedia Content Recommendation](https://mlsanity.com/paper/2207.12236/) (2022)
- [Recommendation Unlearning via Matrix Correction](https://mlsanity.com/paper/2307.15960/) (2023)
- [Differentially private and decentralized randomized power method](https://mlsanity.com/paper/2411.01931/) (2024)
- [How Does Message Passing Improve Collaborative Filtering?](https://mlsanity.com/paper/2404.08660/) (2024)
- [When Newer is Not Better: Does Deep Learning Really Benefit Recommendation From Implicit Feedback?](https://mlsanity.com/paper/2305.01801/) (2023)
- [Graph-based Alignment and Uniformity for Recommendation](https://mlsanity.com/paper/2308.09292/) (2023)
- [SVD-AE: Simple Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/2405.04746/) (2024)
- [Mirroring Users: Towards Building Preference-aligned User Simulator with User Feedback in Recommendation](https://mlsanity.com/paper/2508.18142/) (2025)
- [Fine-tuning Partition-aware Item Similarities for Efficient and Scalable Recommendation](https://mlsanity.com/paper/2207.05959/) (2022)
- [Challenging the Myth of Graph Collaborative Filtering: a Reasoned and Reproducibility-driven Analysis](https://mlsanity.com/paper/2308.00404/) (2023)
- [How Expressive are Graph Neural Networks in Recommendation?](https://mlsanity.com/paper/2308.11127/) (2023)
- [RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2312.16563/) (2023)
- [Frequency-aware Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2402.08426/) (2024)

## Abstract (arXiv)

Graph convolutional networks (GCNs) have recently enabled a popular class of algorithms for collaborative filtering (CF). Nevertheless, the theoretical underpinnings of their empirical successes remain elusive. In this paper, we endeavor to obtain a better understanding of GCN-based CF methods via the lens of graph signal processing. By identifying the critical role of smoothness, a key concept in graph signal processing, we develop a unified graph convolution-based framework for CF. We prove that many existing CF methods are special cases of this framework, including the neighborhood-based methods, low-rank matrix factorization, linear auto-encoders, and LightGCN, corresponding to different low-pass filters. Based on our framework, we then present a simple and computationally efficient CF baseline, which we shall refer to as Graph Filter based Collaborative Filtering (GF-CF). Given an implicit feedback matrix, GF-CF can be obtained in a closed form instead of expensive training with back-propagation. Experiments will show that GF-CF achieves competitive or better performance against deep learning-based methods on three well-known datasets, notably with a 70% performance gain over LightGCN on the Amazon-book dataset.