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MGDCF: Distance Learning via Markov Graph Diffusion for Neural Collaborative Filtering

Jun Hu, Bryan Hooi, Shengsheng Qian, Quan Fang, Changsheng Xu

TL;DR

MGDCF reframes GNN-based collaborative filtering as a distance-learning Markov diffusion process and demonstrates an equivalence between state-of-the-art GNN CF models (such as APPNP and LightGCN) and a traditional 1-layer context-encoding NRL. It introduces MGDN, a unified encoder that can be transformed into MGDN-NRL, clarifying that GNN benefits in CF arise predominantly from optimization guided by ranking losses. The framework extends to a heterogeneous version (Hetero-MGDCF) on user-item graphs and a homogeneous version (Homo-MGDCF) on sparsified item-item graphs, with InfoBPR as a simple yet effective ranking loss that exploits multiple negatives. Extensive experiments on Gowalla, Yelp2018, and Amazon-Book show competitive performance against strong baselines and illustrate the gains from InfoBPR and graph sparsification, providing practical insights into loss design and diffusion-based CF. Together, these results offer an interpretable design direction for GNN-based CF and highlight the crucial role of optimization over regularization in achieving performance gains.

Abstract

Graph Neural Networks (GNNs) have recently been utilized to build Collaborative Filtering (CF) models to predict user preferences based on historical user-item interactions. However, there is relatively little understanding of how GNN-based CF models relate to some traditional Network Representation Learning (NRL) approaches. In this paper, we show the equivalence between some state-of-the-art GNN-based CF models and a traditional 1-layer NRL model based on context encoding. Based on a Markov process that trades off two types of distances, we present Markov Graph Diffusion Collaborative Filtering (MGDCF) to generalize some state-of-the-art GNN-based CF models. Instead of considering the GNN as a trainable black box that propagates learnable user/item vertex embeddings, we treat GNNs as an untrainable Markov process that can construct constant context features of vertices for a traditional NRL model that encodes context features with a fully-connected layer. Such simplification can help us to better understand how GNNs benefit CF models. Especially, it helps us realize that ranking losses play crucial roles in GNN-based CF tasks. With our proposed simple yet powerful ranking loss InfoBPR, the NRL model can still perform well without the context features constructed by GNNs. We conduct experiments to perform detailed analysis on MGDCF.

MGDCF: Distance Learning via Markov Graph Diffusion for Neural Collaborative Filtering

TL;DR

MGDCF reframes GNN-based collaborative filtering as a distance-learning Markov diffusion process and demonstrates an equivalence between state-of-the-art GNN CF models (such as APPNP and LightGCN) and a traditional 1-layer context-encoding NRL. It introduces MGDN, a unified encoder that can be transformed into MGDN-NRL, clarifying that GNN benefits in CF arise predominantly from optimization guided by ranking losses. The framework extends to a heterogeneous version (Hetero-MGDCF) on user-item graphs and a homogeneous version (Homo-MGDCF) on sparsified item-item graphs, with InfoBPR as a simple yet effective ranking loss that exploits multiple negatives. Extensive experiments on Gowalla, Yelp2018, and Amazon-Book show competitive performance against strong baselines and illustrate the gains from InfoBPR and graph sparsification, providing practical insights into loss design and diffusion-based CF. Together, these results offer an interpretable design direction for GNN-based CF and highlight the crucial role of optimization over regularization in achieving performance gains.

Abstract

Graph Neural Networks (GNNs) have recently been utilized to build Collaborative Filtering (CF) models to predict user preferences based on historical user-item interactions. However, there is relatively little understanding of how GNN-based CF models relate to some traditional Network Representation Learning (NRL) approaches. In this paper, we show the equivalence between some state-of-the-art GNN-based CF models and a traditional 1-layer NRL model based on context encoding. Based on a Markov process that trades off two types of distances, we present Markov Graph Diffusion Collaborative Filtering (MGDCF) to generalize some state-of-the-art GNN-based CF models. Instead of considering the GNN as a trainable black box that propagates learnable user/item vertex embeddings, we treat GNNs as an untrainable Markov process that can construct constant context features of vertices for a traditional NRL model that encodes context features with a fully-connected layer. Such simplification can help us to better understand how GNNs benefit CF models. Especially, it helps us realize that ranking losses play crucial roles in GNN-based CF tasks. With our proposed simple yet powerful ranking loss InfoBPR, the NRL model can still perform well without the context features constructed by GNNs. We conduct experiments to perform detailed analysis on MGDCF.
Paper Structure (28 sections, 31 equations, 8 figures, 4 tables)

This paper contains 28 sections, 31 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Traditional Network Representation Learning and Graph Neural Networks
  4. Graph Neural Networks
  5. Neural Collaborative Filtering
  6. Preliminary
  7. Problem Definition
  8. Matrix Factorization and GNN-based Collaborative Filtering
  9. Method
  10. Generalizing State-of-the-art GNN-based CF Models with Markov Graph Diffusion Networks
  11. Distance Learning with Markov Graph Diffusion Networks
  12. Heterogeneous MGDN
  13. Homogeneous MGDN
  14. Explaining MGDN as a Traditional 1-layer NRL Model
  15. Optimization with InfoBPR Loss
  16. ...and 13 more sections

Figures (8)

  • Figure 1: Relation between state-of-the-art GNN-based CF models and a traditional 1-layer NRL model.
  • Figure 2: Overall Framework of MGDCF. MGDCF uses MGDN to learn vertex representations by trading off two types of distances: (1) The left distances (in the purple dashed box) are highly related to the CF task, and minimizing it increases the smoothness of vertex representations over the graph. (2) Minimizing the right distances (in the green dashed box) is against minimizing the left distances, and it can be treated as regularization preventing over-smoothing.
  • Figure 3: Homogeneous MGDCF.
  • Figure 4: Equivalence between some state-of-the-art GNN-based CF models and a traditional 1-layer NRL model.
  • Figure 5: Distribution of affinity weights before sparsification. The orange lines denote the thresholds for sparsification.
  • ...and 3 more figures