Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Turbo-CF: Matrix Decomposition-Free Graph Filtering for Fast Recommendation

Jin-Duk Park, Yong-Min Shin, Won-Yong Shin

TL;DR

This paper tackles the computational bottleneck of graph-filtering based collaborative filtering by eliminating the need for matrix decompositions. It introduces Turbo-CF, a training-free and matrix-decomposition-free method that uses polynomial graph filters on an asymmetrically normalized item-item graph to realize low-pass filtering. By carefully designing edge weights and restricting to low-order polynomial filters, Turbo-CF achieves sub-second runtimes on real-world datasets while delivering competitive recommendation accuracy. The approach leverages GPU-friendly matrix multiplications and offers a practical, scalable baseline for real-time recommendations in dynamic environments.

Abstract

A series of graph filtering (GF)-based collaborative filtering (CF) showcases state-of-the-art performance on the recommendation accuracy by using a low-pass filter (LPF) without a training process. However, conventional GF-based CF approaches mostly perform matrix decomposition on the item-item similarity graph to realize the ideal LPF, which results in a non-trivial computational cost and thus makes them less practical in scenarios where rapid recommendations are essential. In this paper, we propose Turbo-CF, a GF-based CF method that is both training-free and matrix decomposition-free. Turbo-CF employs a polynomial graph filter to circumvent the issue of expensive matrix decompositions, enabling us to make full use of modern computer hardware components (i.e., GPU). Specifically, Turbo-CF first constructs an item-item similarity graph whose edge weights are effectively regulated. Then, our own polynomial LPFs are designed to retain only low-frequency signals without explicit matrix decompositions. We demonstrate that Turbo-CF is extremely fast yet accurate, achieving a runtime of less than 1 second on real-world benchmark datasets while achieving recommendation accuracies comparable to best competitors.

Turbo-CF: Matrix Decomposition-Free Graph Filtering for Fast Recommendation

TL;DR

This paper tackles the computational bottleneck of graph-filtering based collaborative filtering by eliminating the need for matrix decompositions. It introduces Turbo-CF, a training-free and matrix-decomposition-free method that uses polynomial graph filters on an asymmetrically normalized item-item graph to realize low-pass filtering. By carefully designing edge weights and restricting to low-order polynomial filters, Turbo-CF achieves sub-second runtimes on real-world datasets while delivering competitive recommendation accuracy. The approach leverages GPU-friendly matrix multiplications and offers a practical, scalable baseline for real-time recommendations in dynamic environments.

Abstract

A series of graph filtering (GF)-based collaborative filtering (CF) showcases state-of-the-art performance on the recommendation accuracy by using a low-pass filter (LPF) without a training process. However, conventional GF-based CF approaches mostly perform matrix decomposition on the item-item similarity graph to realize the ideal LPF, which results in a non-trivial computational cost and thus makes them less practical in scenarios where rapid recommendations are essential. In this paper, we propose Turbo-CF, a GF-based CF method that is both training-free and matrix decomposition-free. Turbo-CF employs a polynomial graph filter to circumvent the issue of expensive matrix decompositions, enabling us to make full use of modern computer hardware components (i.e., GPU). Specifically, Turbo-CF first constructs an item-item similarity graph whose edge weights are effectively regulated. Then, our own polynomial LPFs are designed to retain only low-frequency signals without explicit matrix decompositions. We demonstrate that Turbo-CF is extremely fast yet accurate, achieving a runtime of less than 1 second on real-world benchmark datasets while achieving recommendation accuracies comparable to best competitors.
Paper Structure (15 sections, 1 theorem, 7 equations, 4 figures, 4 tables)

This paper contains 15 sections, 1 theorem, 7 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Methodology
  4. Motivation and Challenge
  5. Proposed Method: Turbo-CF
  6. Graph construction
  7. Polynomial GF
  8. Filter design
  9. Experimental results and Analyses
  10. Experimental Settings
  11. Runtime Comparison
  12. Recommendation Accuracy
  13. Effect of Polynomial Graph Filters
  14. Sensitivity Analysis
  15. Conclusions

Key Result

theorem 1

The matrix polynomial $\sum_{k=1}^K{a_k}\bar{P}^k$ is a graph filter for graph $\bar{P}$ with the frequency response function of $h(\lambda) = \sum_{k=1}^K{a_k}(1 - \lambda)^k$.

Figures (4)

  • Figure 1: Accuracy versus runtime among Turbo-CF and other benchmark methods on the Gowalla dataset.
  • Figure 2: The schematic overview of Turbo-CF. The graph signals are smoothed by using polynomial LPFs in Turbo-CF.
  • Figure 3: Frequency response functions of three polynomial LPFs. In Figure 3(c), the dotted blue line corresponds to the ideal LPF $h(\lambda) = {\bf 1}_{\lambda\le0.1}$.
  • Figure 4: The effect of two hyperparameters on the Recall@20 for the Gowalla dataset.

Theorems & Definitions (3)

  • definition 1
  • definition 2
  • theorem 1