# On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering

arXiv: https://arxiv.org/abs/2306.03624 · HTML: https://mlsanity.com/paper/2306.03624/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 54 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2112.08679/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [RecBole: Towards a Unified, Comprehensive and Efficient Framework for Recommendation Algorithms](https://mlsanity.com/paper/2011.01731/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Disentangled Graph Collaborative Filtering](https://mlsanity.com/paper/2007.01764/) (2020)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning](https://mlsanity.com/paper/2202.06200/) (2022)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion](https://mlsanity.com/paper/1905.01866/) (2019)
- [Towards Representation Alignment and Uniformity in Collaborative Filtering](https://mlsanity.com/paper/2206.12811/) (2022)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)
- [How Powerful is Graph Convolution for Recommendation?](https://mlsanity.com/paper/2108.07567/) (2021)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Efficiently Leveraging Multi-level User Intent for Session-based Recommendation via Atten-Mixer Network](https://mlsanity.com/paper/2206.12781/) (2022)
- [Continual Learning on Dynamic Graphs via Parameter Isolation](https://mlsanity.com/paper/2305.13825/) (2023)
- [Collaborative Memory Network for Recommendation Systems](https://mlsanity.com/paper/1804.10862/) (2018)

## Built on by (most cited first, 9 of 9)

- [Towards Graph Contrastive Learning: A Survey and Beyond](https://mlsanity.com/paper/2405.11868/) (2024)
- [Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfer](https://mlsanity.com/paper/2308.09499/) (2023)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [Boosting Disfluency Detection with Large Language Model as Disfluency Generator](https://mlsanity.com/paper/2403.08229/) (2024)
- [GSPRec: On Improving Item Representations in Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2505.11552/) (2025)
- [On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signals](https://mlsanity.com/paper/2509.10874/) (2025)
- [Lighter-X: An Efficient and Plug-and-play Strategy for Graph-based Recommendation through Decoupled Propagation](https://mlsanity.com/paper/2510.10105/) (2025)
- [How Do Graph Signals Affect Recommendation: Unveiling the Mystery of Low and High-Frequency Graph Signals](https://mlsanity.com/paper/2512.15744/) (2025)
- [DualSpectralCF: Training-Free Sign-Aware Spectral Collaborative Filtering](https://mlsanity.com/paper/2608.10247/) (2026)

## Abstract (arXiv)

Collaborative filtering (CF) is an important research direction in recommender systems that aims to make recommendations given the information on user-item interactions. Graph CF has attracted more and more attention in recent years due to its effectiveness in leveraging high-order information in the user-item bipartite graph for better recommendations. Specifically, recent studies show the success of graph neural networks (GNN) for CF is attributed to its low-pass filtering effects. However, current researches lack a study of how different signal components contributes to recommendations, and how to design strategies to properly use them well. To this end, from the view of spectral transformation, we analyze the important factors that a graph filter should consider to achieve better performance. Based on the discoveries, we design JGCF, an efficient and effective method for CF based on Jacobi polynomial bases and frequency decomposition strategies. Extensive experiments on four widely used public datasets show the effectiveness and efficiency of the proposed methods, which brings at most 27.06% performance gain on Alibaba-iFashion. Besides, the experimental results also show that JGCF is better at handling sparse datasets, which shows potential in making recommendations for cold-start users.