Directed Graph Convolutional Network

Zekun Tong, Yuxuan Liang, Changsheng Sun, David S. Rosenblum, A. Lim

Main figure for Directed Graph Convolutional Network

Abstract

Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph convolution to directed graphs by using first- and second-order proximity, which can not only retain the connection properties of the directed graph, but also expand the receptive field of the convolution operation. A new GCN model, called DGCN, is then designed to learn representations on the directed graph, leveraging both the first- and second-order proximity information. We empirically show the fact that GCNs working only with DGCNs can encode more useful information from graph and help achieve better performance when generalized to other models. Moreover, extensive experiments on citation networks and co-purchase datasets demonstrate the superiority of our model against the state-of-the-art methods.

Benchmark Results

Tested on 3 datasets Non-standard metric on 1 dataset

Tables show presented results in global context (best 3 papers + GCN + MLP).

Classic

#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #448 446 places worse
0.9000 ±0.0130
actual #2 vs paper #448 446 places worse
paper 0.9000 ±0.0130

Improvement within reported uncertainty; not highlighted.

paper 0.9000 ±0.0130 Δ at pub 0.0030 Δ today 0.0669
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #434 426 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #434 426 places worse
paper 0.9040 ±0.0150
50
SGC
actual #50 vs paper #465 415 places worse
0.9511 ±0.0009
best reported
actual #50 vs paper #465 415 places worse
paper 0.8940 ±0.0140
56
GraphSAGE
actual #56 vs paper #455 399 places worse
0.9508 ±0.0026
best reported
actual #56 vs paper #455 399 places worse
paper 0.8980 ±0.0190
119
ChebNet
actual #119 vs paper #524 405 places worse
0.9377 ±0.0032
best reported
actual #119 vs paper #524 405 places worse
paper 0.8250 ±0.0240
paper 0.8250 ±0.0240 Δ today 0.1127
390
MLP
0.9128 ±0.0063
411
DGCN
0.9080 ±0.0110
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #407 405 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #407 405 places worse
paper 0.8190 ±0.0190
3
GAT
actual #3 vs paper #415 412 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #415 412 places worse
paper 0.8120 ±0.0250
paper 0.8120 ±0.0250 Δ at pub 0.0060 Δ today 0.1278
8
SAGE
0.9351 ±0.0006
46
GraphSAGE
actual #46 vs paper #427 381 places worse
0.8040 ±0.0250
actual #46 vs paper #427 381 places worse
paper 0.8040 ±0.0250

Improvement within reported uncertainty; not highlighted.

paper 0.8040 ±0.0250 Δ at pub 0.0020 Δ today 0.1080
82
SGC
actual #82 vs paper #428 346 places worse
0.9022 ±0.0021
best reported
actual #82 vs paper #428 346 places worse
paper 0.8020 ±0.0120
paper 0.8020 ±0.0120 Δ at pub 0.0160 Δ today 0.1002
216
ChebNet
actual #216 vs paper #463 247 places worse
0.8782 ±0.0072
best reported
actual #216 vs paper #463 247 places worse
paper 0.7290 ±0.0300
paper 0.7290 ±0.0300 Δ today 0.1492
320
MLP
0.8463
405
DGCN
0.8200 ±0.0170
This paper

Heterogeneous Graph Benchmarks

DBLP

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is Micro-F1. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑Paper
1
HG-SCM
0.9490 ±0.0015
2
SeHGNN
0.9489 ±0.0018
3
AdvSynGNN
0.9486 ±0.0012
31
GAT
actual #31 vs paper #111 80 places worse
0.7180 ±0.0260
actual #31 vs paper #111 80 places worse
paper 0.7180 ±0.0260
paper 0.7180 ±0.0260 Δ at pub 0.0570 Δ today 0.1679
36
GCN
actual #36 vs paper #113 77 places worse
0.7150 ±0.0270
actual #36 vs paper #113 77 places worse
paper 0.7150 ±0.0270
paper 0.7150 ±0.0270 Δ at pub 0.1220 Δ today 0.1608
61
SGC
actual #61 vs paper #115 54 places worse
0.8170
best reported
actual #61 vs paper #115 54 places worse
paper 0.6920 ±0.0280
paper 0.6920 ±0.0280 Δ today 0.1250
65
MLP
0.8118 ±0.0020
105
GraphSAGE
actual #105 vs paper #115 10 places worse
0.7455 ±0.0061
best reported
actual #105 vs paper #115 10 places worse
paper 0.6810 ±0.0250
paper 0.6810 ±0.0250 Δ today 0.0645
109
DGCN
0.7250 ±0.0250
This paper
114
SGC+DGCN
0.7110 ±0.0230
This paper
118
ChebNet
0.6400 ±0.0280
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere