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Graph Edge Representation via Tensor Product Graph Convolutional Representation

Bo Jiang, Sheng Ge, Ziyan Zhang, Beibei Wang, Jin Tang, Bin Luo

TL;DR

The proposed TPGC provides a complementary model to traditional graph convolutions (GCs) to address the more general graph data analysis with both node and edge features and demonstrates the effectiveness of the proposed TPGC.

Abstract

Graph Convolutional Networks (GCNs) have been widely studied. The core of GCNs is the definition of convolution operators on graphs. However, existing Graph Convolution (GC) operators are mainly defined on adjacency matrix and node features and generally focus on obtaining effective node embeddings which cannot be utilized to address the graphs with (high-dimensional) edge features. To address this problem, by leveraging tensor contraction representation and tensor product graph diffusion theories, this paper analogously defines an effective convolution operator on graphs with edge features which is named as Tensor Product Graph Convolution (TPGC). The proposed TPGC aims to obtain effective edge embeddings. It provides a complementary model to traditional graph convolutions (GCs) to address the more general graph data analysis with both node and edge features. Experimental results on several graph learning tasks demonstrate the effectiveness of the proposed TPGC.

Graph Edge Representation via Tensor Product Graph Convolutional Representation

TL;DR

The proposed TPGC provides a complementary model to traditional graph convolutions (GCs) to address the more general graph data analysis with both node and edge features and demonstrates the effectiveness of the proposed TPGC.

Abstract

Graph Convolutional Networks (GCNs) have been widely studied. The core of GCNs is the definition of convolution operators on graphs. However, existing Graph Convolution (GC) operators are mainly defined on adjacency matrix and node features and generally focus on obtaining effective node embeddings which cannot be utilized to address the graphs with (high-dimensional) edge features. To address this problem, by leveraging tensor contraction representation and tensor product graph diffusion theories, this paper analogously defines an effective convolution operator on graphs with edge features which is named as Tensor Product Graph Convolution (TPGC). The proposed TPGC aims to obtain effective edge embeddings. It provides a complementary model to traditional graph convolutions (GCs) to address the more general graph data analysis with both node and edge features. Experimental results on several graph learning tasks demonstrate the effectiveness of the proposed TPGC.
Paper Structure (18 sections, 8 equations, 5 figures, 8 tables)

This paper contains 18 sections, 8 equations, 5 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Revisiting GC from Dual Linear Transformations
  5. TPGC Representation
  6. Tensor Contraction Layer (TCL)
  7. From TCL to TPGC
  8. Complexity Analysis
  9. Comparison with Related Works
  10. Edge Tensor-Graph Convolutional Network
  11. Experiments
  12. Datasets
  13. Semi-supervised Node Classification
  14. Inductive Learning
  15. Link Prediction
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Illustration of GC operation.
  • Figure 2: Illustration of the proposed TPGC.
  • Figure 3: The overall framework of ET-GCN and ET-GAT.
  • Figure 4: Comparison results for multiple graph learning.
  • Figure 5: Comparison results of homophily of the learnable adjacency matrix obtained by TPGC.