# PolyCF: Towards the Optimal Spectral Graph Filters for Collaborative Filtering

arXiv: https://arxiv.org/abs/2401.12590 · HTML: https://mlsanity.com/paper/2401.12590/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2024.

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

- [Towards Graph Contrastive Learning: A Survey and Beyond](https://mlsanity.com/paper/2405.11868/) (2024)
- [S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain](https://mlsanity.com/paper/2501.00384/) (2024)
- [Memory Is No Longer a Bottleneck: Memory-Efficient Graph Filtering for Scalable Collaborative Filtering](https://mlsanity.com/paper/2606.21540/) (2026)
- [Lighter-X: An Efficient and Plug-and-play Strategy for Graph-based Recommendation through Decoupled Propagation](https://mlsanity.com/paper/2510.10105/) (2025)
- [LLM-driven Multimodal Recommendation](https://mlsanity.com/paper/2602.05474/) (2026)
- [DualSpectralCF: Training-Free Sign-Aware Spectral Collaborative Filtering](https://mlsanity.com/paper/2608.10247/) (2026)
- [Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Study](https://mlsanity.com/paper/2609.28979/) (2026)

## Abstract (arXiv)

Collaborative Filtering (CF) is a pivotal research area in recommender systems that capitalizes on collaborative similarities between users and items to provide personalized recommendations. With the remarkable achievements of node embedding-based Graph Neural Networks (GNNs), we explore the upper bounds of expressiveness inherent to embedding-based methodologies and tackle the challenges by reframing the CF task as a graph signal processing problem. To this end, we propose PolyCF, a flexible graph signal filter that leverages polynomial graph filters to process interaction signals. PolyCF exhibits the capability to capture spectral features across multiple eigenspaces through a series of Generalized Gram filters and is able to approximate the optimal polynomial response function for recovering missing interactions. A graph optimization objective and a pair-wise ranking objective are jointly used to optimize the parameters of the convolution kernel. Experiments on three widely adopted datasets demonstrate the superiority of PolyCF over current state-of-the-art CF methods. Moreover, comprehensive studies empirically validate each component's efficacy in the proposed PolyCF.