How Do Graph Signals Affect Recommendation: Unveiling the Mystery of Low and High-Frequency Graph Signals

TL;DR

The paper investigates how graph signals at different frequencies affect recommendation performance. It proves that low- and high-frequency signals with the same waveform magnitude impact recommendations equivalently by smoothing user-item similarities, and introduces a frequency signal scaler to flexibly shape filters for any GNN. To address embedding limitations, it proposes a space flip to recover hidden high-frequency characteristics and presents SimGCF, a plug-in that achieves state-of-the-art results on four public datasets. The work combines theoretical analysis with extensive experiments to offer practical, scalable tools for leveraging graph signals in recommender systems.

Abstract

Spectral graph neural networks (GNNs) are highly effective in modeling graph signals, with their success in recommendation often attributed to low-pass filtering. However, recent studies highlight the importance of high-frequency signals. The role of low-frequency and high-frequency graph signals in recommendation remains unclear. This paper aims to bridge this gap by investigating the influence of graph signals on recommendation performance. We theoretically prove that the effects of low-frequency and high-frequency graph signals are equivalent in recommendation tasks, as both contribute by smoothing the similarities between user-item pairs. To leverage this insight, we propose a frequency signal scaler, a plug-and-play module that adjusts the graph signal filter function to fine-tune the smoothness between user-item pairs, making it compatible with any GNN model. Additionally, we identify and prove that graph embedding-based methods cannot fully capture the characteristics of graph signals. To address this limitation, a space flip method is introduced to restore the expressive power of graph embeddings. Remarkably, we demonstrate that either low-frequency or high-frequency graph signals alone are sufficient for effective recommendations. Extensive experiments on four public datasets validate the effectiveness of our proposed methods. Code is avaliable at https://github.com/mojosey/SimGCF.

Figures (12)

• Figure 1: Analyze the impact of low-frequency and high-frequency graph signals on recommendation. (a) The waveforms of low-pass function in quadrant I and high-pass function in quadrant III. (b) The performance of low-pass and high-pass GNNs on four datasets, evaluated on Recall@20.
• Figure 2: The Characteristics of graph signals and graph embedding signals.
• Figure 3: The performance of LightGCN with different waveforms on Gowalla.
• Figure 4: The framework of SimGCF. The low-frequency SimGCF performs frequency signal scaling on the original $f(\lambda)$, and the high-frequency SimGCF also needs to perform space flip on the embedding after scaling.
• Figure 5: Analysis of $\mu$, $\alpha$ and $\beta$.