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Collaborative Filtering Meets Spectrum Shift: Connecting User-Item Interaction with Graph-Structured Side Information

Yunhang He, Cong Xu, Jun Wang, Wei Zhang

TL;DR

This work identifies a spectrum shift phenomenon that occurs when graph-structured side information is integrated into the user-item interaction graph, causing the augmented adjacency spectrum to move away from the traditional full range $[-1,1]$. It introduces Spectrum Shift Correction (SSC), a simple, plug-and-play transformation $g_+(\lambda)=g((\lambda-\mu)/\Delta)$ (with $\phi(\tilde{A}_+)=(\tilde{A}_+-\mu I)/\Delta$) to realign the spectrum without additional computation, enabling standard spectral GNNs to effectively leverage side information. SSC is demonstrated to significantly improve LightGCN and JGCF across multimodal and social recommendation tasks (up to $23\%$ relative gains) while exhibiting robustness to noise and only modest hyperparameter tuning. The approach unifies the use of graph-structured side information with spectral methods, offering practical, efficient enhancements for large-scale recommender systems. The results underscore SSC's potential to broaden the applicability of spectral GNNs by reconciling spectrum mismatches introduced by augmented graphs.

Abstract

Graph Neural Networks (GNNs) have demonstrated their superiority in collaborative filtering, where the user-item (U-I) interaction bipartite graph serves as the fundamental data format. However, when graph-structured side information (e.g., multimodal similarity graphs or social networks) is integrated into the U-I bipartite graph, existing graph collaborative filtering methods fall short of achieving satisfactory performance. We quantitatively analyze this problem from a spectral perspective. Recall that a bipartite graph possesses a full spectrum within the range of [-1, 1], with the highest frequency exactly achievable at -1 and the lowest frequency at 1; however, we observe as more side information is incorporated, the highest frequency of the augmented adjacency matrix progressively shifts rightward. This spectrum shift phenomenon has caused previous approaches built for the full spectrum [-1, 1] to assign mismatched importance to different frequencies. To this end, we propose Spectrum Shift Correction (dubbed SSC), incorporating shifting and scaling factors to enable spectral GNNs to adapt to the shifted spectrum. Unlike previous paradigms of leveraging side information, which necessitate tailored designs for diverse data types, SSC directly connects traditional graph collaborative filtering with any graph-structured side information. Experiments on social and multimodal recommendation demonstrate the effectiveness of SSC, achieving relative improvements of up to 23% without incurring any additional computational overhead. Our code is available at https://github.com/yhhe2004/SSC-KDD.

Collaborative Filtering Meets Spectrum Shift: Connecting User-Item Interaction with Graph-Structured Side Information

TL;DR

This work identifies a spectrum shift phenomenon that occurs when graph-structured side information is integrated into the user-item interaction graph, causing the augmented adjacency spectrum to move away from the traditional full range . It introduces Spectrum Shift Correction (SSC), a simple, plug-and-play transformation (with ) to realign the spectrum without additional computation, enabling standard spectral GNNs to effectively leverage side information. SSC is demonstrated to significantly improve LightGCN and JGCF across multimodal and social recommendation tasks (up to relative gains) while exhibiting robustness to noise and only modest hyperparameter tuning. The approach unifies the use of graph-structured side information with spectral methods, offering practical, efficient enhancements for large-scale recommender systems. The results underscore SSC's potential to broaden the applicability of spectral GNNs by reconciling spectrum mismatches introduced by augmented graphs.

Abstract

Graph Neural Networks (GNNs) have demonstrated their superiority in collaborative filtering, where the user-item (U-I) interaction bipartite graph serves as the fundamental data format. However, when graph-structured side information (e.g., multimodal similarity graphs or social networks) is integrated into the U-I bipartite graph, existing graph collaborative filtering methods fall short of achieving satisfactory performance. We quantitatively analyze this problem from a spectral perspective. Recall that a bipartite graph possesses a full spectrum within the range of [-1, 1], with the highest frequency exactly achievable at -1 and the lowest frequency at 1; however, we observe as more side information is incorporated, the highest frequency of the augmented adjacency matrix progressively shifts rightward. This spectrum shift phenomenon has caused previous approaches built for the full spectrum [-1, 1] to assign mismatched importance to different frequencies. To this end, we propose Spectrum Shift Correction (dubbed SSC), incorporating shifting and scaling factors to enable spectral GNNs to adapt to the shifted spectrum. Unlike previous paradigms of leveraging side information, which necessitate tailored designs for diverse data types, SSC directly connects traditional graph collaborative filtering with any graph-structured side information. Experiments on social and multimodal recommendation demonstrate the effectiveness of SSC, achieving relative improvements of up to 23% without incurring any additional computational overhead. Our code is available at https://github.com/yhhe2004/SSC-KDD.

Paper Structure

This paper contains 33 sections, 1 theorem, 17 equations, 6 figures, 11 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Collaborative Filtering
  4. Spectral Graph Neural Networks
  5. Graph-Structured Side Information
  6. Spectrum Analysis on Augmented Graphs
  7. Oracle Spectrum Importance
  8. Spectrum Shift Phenomenon
  9. Spectrum Shift Correction
  10. Simple yet Effective Method
  11. Applications
  12. Experiments
  13. Experiment Setup
  14. Overall Performance Comparison (RQ1 & RQ2)
  15. SSC Visualization (RQ3)
  16. ...and 18 more sections

Key Result

theorem 1

Let $S(\kappa) \in \mathbb{R}^{|\mathcal{U}| \times |\mathcal{U}|}$ denote a symmetric matrix with non-zero row sums. For the augmented adjacency matrix $\tilde{A}_+$, its maximum eigenvalue value $\lambda_{\max}(\kappa) \equiv 1$. Moreover, when $\kappa \rightarrow +\infty$ The same results can be drawn for I-I graphs.

Figures (6)

  • Figure 1: The integration of (a) graph-structured side information results in (b) spectrum shift. LightGCN and JGCF are tailored for the full spectrum of $\tilde{A}$, which inevitably results in a mismatch when applied to the augmented adjacency matrix $\tilde{A}_+$.
  • Figure 2: Oracle spectrum importance $\mathcal{R}(U_{:, \lambda}; B)$ as more side information is integrated (i.e., $\kappa$ increases).
  • Figure 3: Pipeline of SSC.
  • Figure 4: Overall performance comparison for social recommendation.
  • Figure 5: Model performance under progressively increasing levels of noise intensity $\delta$.
  • ...and 1 more figures

Theorems & Definitions (1)

  • theorem 1