Frequency-aware Graph Signal Processing for Collaborative Filtering

TL;DR

FaGSP advances collaborative filtering by introducing frequency-aware graph signal processing that simultaneously captures user/item unique and common characteristics and leverages high-order neighborhood information. It comprises a Cascaded Filter Module (high-pass followed by low-pass) to highlight unique traits and a Parallel Filter Module (dual low-pass filters) to exploit high-order neighborhoods, combined linearly for prediction. Across six public datasets, FaGSP achieves state-of-the-art accuracy with competitive training efficiency, and ablations confirm the necessity of each module. The work offers a practical, parameter-efficient alternative to deep GCNs for scalable, effective recommendations.

Abstract

Graph Signal Processing (GSP) based recommendation algorithms have recently attracted lots of attention due to its high efficiency. However, these methods failed to consider the importance of various interactions that reflect unique user/item characteristics and failed to utilize user and item high-order neighborhood information to model user preference, thus leading to sub-optimal performance. To address the above issues, we propose a frequency-aware graph signal processing method (FaGSP) for collaborative filtering. Firstly, we design a Cascaded Filter Module, consisting of an ideal high-pass filter and an ideal low-pass filter that work in a successive manner, to capture both unique and common user/item characteristics to more accurately model user preference. Then, we devise a Parallel Filter Module, consisting of two low-pass filters that can easily capture the hierarchy of neighborhood, to fully utilize high-order neighborhood information of users/items for more accurate user preference modeling. Finally, we combine these two modules via a linear model to further improve recommendation accuracy. Extensive experiments on six public datasets demonstrate the superiority of our method from the perspectives of prediction accuracy and training efficiency compared with state-of-the-art GCN-based recommendation methods and GSP-based recommendation methods.

Figures (5)

• Figure 1: A toy example of user interaction prediction with 4 users and 4 items. (a) is the original interaction matrix, (b) and (c) are the prediction of the ideal low-pass filter and linear filter in GF-CF respectively. (d) is the enhanced interaction matrix, (e)--(f) are the predictions of the Cascaded Filter Module and Parallel Filter Module in FaGSP respectively. For ideal high-pass filter to enhance interactions in (d), we set $p_1=2$, $q=0.65$, and $\alpha_1=0.5$. For ideal low-pass filter in (b) and (d), we set $p_2=2$. In Parallel Filter Module, we only consider item high-order neighborhood information for the ease of presentation.
• Figure 2: The frequency response functions $h(\lambda)=1-\lambda^{k_1}$ with respect to different order $k_1$ ranging from 1 to 5.
• Figure 3: Visualization of consistency between user historical and predicted preference.
• Figure 4: The average training time (5 times) of FaGSP and other methods on ML1M.
• Figure 5: The sensitivity analysis of two hyper-parameters on ML1M dataset: Number of High Frequency Component $p_1$ and Order of Item High-order Neighborhood Filter (IHNF) $k_1$.

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof