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Just Propagate: Unifying Matrix Factorization, Network Embedding, and LightGCN for Link Prediction

Haoxin Liu

TL;DR

A unified framework for link prediction that covers matrix factorization and representative network embedding and graph neural network methods is proposed that could deepen the understanding and inspire novel designs for link prediction methods.

Abstract

Link prediction is a fundamental task in graph analysis. Despite the success of various graph-based machine learning models for link prediction, there lacks a general understanding of different models. In this paper, we propose a unified framework for link prediction that covers matrix factorization and representative network embedding and graph neural network methods. Our preliminary methodological and empirical analyses further reveal several key design factors based on our unified framework. We believe our results could deepen our understanding and inspire novel designs for link prediction methods.

Just Propagate: Unifying Matrix Factorization, Network Embedding, and LightGCN for Link Prediction

TL;DR

A unified framework for link prediction that covers matrix factorization and representative network embedding and graph neural network methods is proposed that could deepen the understanding and inspire novel designs for link prediction methods.

Abstract

Link prediction is a fundamental task in graph analysis. Despite the success of various graph-based machine learning models for link prediction, there lacks a general understanding of different models. In this paper, we propose a unified framework for link prediction that covers matrix factorization and representative network embedding and graph neural network methods. Our preliminary methodological and empirical analyses further reveal several key design factors based on our unified framework. We believe our results could deepen our understanding and inspire novel designs for link prediction methods.

Paper Structure

This paper contains 19 sections, 15 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Loss Function
  5. A Brief Introduction to Considered Link Prediction Models
  6. Our Proposed Framework
  7. The Unified Framework
  8. Revisiting the Existing Link Prediction Methods
  9. Conclusion
  10. Main Notations
  11. Proof
  12. Loss
  13. LightGCN Derivation
  14. Detailed Correspondence of Link Prediction Models
  15. Experimental Settings
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The analysis results of MF and LightGCN. (a) The mean value of $\mathcal{K}_+$ as the optimization step increases; (b) The Frobenius norm of $\mathbf{X}$ as the optimization step increases; (c) The Frobenius norm $\left\| \mathbf{X} \right\|_F$ for LightGCN as the optimization substeps increase.