ICML 2023

Feature Expansion for Graph Neural Networks

Jiaqi Sun, Lin Zhang, Guan-Hong Chen, Kun Zhang, Peng Xu, Yujiu Yang

Main figure for Feature Expansion for Graph Neural Networks

Abstract

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

Benchmark Results

Tested on 8 datasets 8 baseline values reported too low Non-standard metric on 4 datasets

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

Classic

Cora

Global leaderboard →
Non-default metric. This paper reports Accuracy (micro F1 per L1108); the dataset default is Accuracy. Values below use Accuracy (micro F1 per L1108) only.
#ModelAccuracy (micro F1 per L1108) ↑Paper
1
FE-GNN (C)
0.8945 ±0.0022
This paper

CiteSeer

Global leaderboard →

Default metric is Accuracy. The paper reports 11 values on Accuracy and 1 value on Accuracy (micro F1 per L1108) .

#ModelAccuracy ↑ defaultAccuracy (micro F1 per L1108) ↑Paper
1
CNA
0.9575 ± 0.0058
—
2
IS-GIB
0.9390 ± 0.0187
—
3
EERM
0.9112 ± 0.0145
—
15
GNN-LF
0.8366 ± 0.0006
—
Accuracy (micro F1 per L1108) —
This paper
16
GNN-HF
0.8356 ± 0.0010
—
Accuracy (micro F1 per L1108) —
This paper
18
FE-GNN (C)
—
0.8196 ± 0.0023
Accuracy (micro F1 per L1108) 0.8196 ± 0.0023
This paper
20
APPNP
0.8142 ±0.0026
—
Accuracy (micro F1 per L1108) —
paper 0.8142 ±0.0026
paper 0.8142 ±0.0026 Δ at pub 0.0092
32
GPRGNN
0.7857 ±0.0031
—
Accuracy (micro F1 per L1108) —
paper 0.7857 ±0.0031
35
GAT
0.8080 ±0.0026
—
Accuracy (micro F1 per L1108) —
paper 0.8080 ±0.0026

Improvement within reported uncertainty; not highlighted.

paper 0.8080 ±0.0026 Δ at pub 0.0067
36
GCNII
0.8076 ±0.0030
—
Accuracy (micro F1 per L1108) —
paper 0.8076 ±0.0030
paper 0.8076 ±0.0030 Δ at pub 0.0565
44
GCN
0.8033 ±0.0088
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.7931 ±0.0046

Difference within reported uncertainty; not counted as underperformance.

paper 0.7931 ±0.0046 Δ at pub 0.0012 Δ today 0.0102
58
BernNet
0.7934 ±0.0032
—
Accuracy (micro F1 per L1108) —
paper 0.7934 ±0.0032
paper 0.7934 ±0.0032 Δ at pub 0.2582
59
ADA-UGNN
0.7934 ± 0.0009
—
Accuracy (micro F1 per L1108) —
This paper
61
GraphSAGE
0.7923 ±0.0053
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.7920 ±0.0042

Difference within reported uncertainty; not counted as underperformance.

paper 0.7920 ±0.0042 Δ at pub 0.0003
90
ChebyNet
0.7797 ±0.0036
—
Accuracy (micro F1 per L1108) —
paper 0.7797 ±0.0036
paper 0.7797 ±0.0036 Δ at pub 0.0817
259
SAGE
0.7361 ± 0.0190
—
350
MLP
0.7289 ± 0.0010
—
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
17
APPNP
actual #17 vs paper #156 139 places worse
0.9355 ±0.0060
best reported
actual #17 vs paper #156 139 places worse
paper 0.8816 ±0.0014
18
GCN
actual #18 vs paper #218 200 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #218 200 places worse
paper 0.8671 ±0.0018
20
GAT
actual #20 vs paper #220 200 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #220 200 places worse
paper 0.8669 ±0.0014
68
ADA-UGNN
0.9008 ±0.0005
This paper
93
BernNet
actual #93 vs paper #93
0.8933 ±0.0007
actual #93 vs paper #93
paper 0.8933 ±0.0007
paper 0.8933 ±0.0007 Δ at pub 0.1401
101
GPRGNN
actual #101 vs paper #101
0.8911 ±0.0008
actual #101 vs paper #101
paper 0.8911 ±0.0008
paper 0.8911 ±0.0008 Δ at pub 0.0997
107
ChebyNet
actual #107 vs paper #107
0.8904 ±0.0008
actual #107 vs paper #107
paper 0.8904 ±0.0008
paper 0.8904 ±0.0008 Δ at pub 0.1464
116
SAGE
0.8881 ±0.0015
125
GraphSAGE
actual #125 vs paper #180 55 places worse
0.8765 ±0.0014
actual #125 vs paper #180 55 places worse
paper 0.8765 ±0.0014
paper 0.8765 ±0.0014 Δ at pub 0.0055 Δ today 0.0099
163
GNN-HF
0.8783 ±0.0010
This paper
168
GNN-LF
0.8779 ±0.0005
This paper
210
MLP
actual #210 vs paper #255 45 places worse
0.8690 ±0.0074
best reported
actual #210 vs paper #255 45 places worse
paper 0.8511 ±0.0026
paper 0.8511 ±0.0026 Δ at pub 0.0127 Δ today 0.0179

Amazon-Photo

Global leaderboard →

Default metric is Accuracy. The paper reports 1 value on Accuracy and 1 value on Accuracy (micro F1 per L1108) .

#ModelAccuracy ↑ defaultAccuracy (micro F1 per L1108) ↑Paper
1
GraphTARIF
0.9703 ± 0.0019
—
2
GAT
0.9669 ± 0.0014
—
3
GAT+T
0.9660 ± 0.0007
—
7
SAGE
0.9643 ± 0.0027
—
38
FE-GNN (C)
—
0.9536 ± 0.0014
Accuracy (micro F1 per L1108) 0.9536 ± 0.0014
This paper
68
C (orthogonal)
0.9484 ± 0.0079
—
Accuracy (micro F1 per L1108) —
This paper
390
MLP
0.9128 ± 0.0063
—

Amazon-Computers

Global leaderboard →
Non-default metric. This paper reports Accuracy (micro F1 per L1108); the dataset default is Accuracy. Values below use Accuracy (micro F1 per L1108) only.
#ModelAccuracy (micro F1 per L1108) ↑Paper
1
FE-GNN (C)
0.9079 ±0.0008
This paper

Heterophilic Graphs

Actor

Global leaderboard →

Default metric is Accuracy. The paper reports 8 values on Accuracy and 5 values on Accuracy (micro F1 per L1108) .

#ModelAccuracy ↑ defaultAccuracy (micro F1 per L1108) ↑Paper
1
DiGGR
0.4535 ± 0.0353
—
2
TRIGON
0.4402 ± 0.0028
—
3
DoG
0.4320 ± 0.0120
—
11
GNN-HF
—
0.4247 ± 0.0007
Accuracy (micro F1 per L1108) 0.4247 ± 0.0007
This paper
17
GNN-LF
0.4197 ± 0.0006
—
Accuracy (micro F1 per L1108) —
This paper
29
ADA-UGNN
—
0.4138 ± 0.0012
Accuracy (micro F1 per L1108) 0.4138 ± 0.0012
This paper
38
GCNII
0.3861 ±0.0026
—
Accuracy (micro F1 per L1108) —
paper 0.3861 ±0.0026

Improvement within reported uncertainty; not highlighted.

paper 0.3861 ±0.0026 Δ at pub 0.0117
40
FE-GNN (C)
—
0.4054 ± 0.0015
Accuracy (micro F1 per L1108) 0.4054 ± 0.0015
This paper
41
APPNP
0.3990 ±0.0025
—
Accuracy (micro F1 per L1108) —
paper 0.3990 ±0.0025

Improvement within reported uncertainty; not highlighted.

paper 0.3990 ±0.0025 Δ at pub 0.0014 Δ today 0.0056
42
MLP
0.4026 ±0.0108
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.3899 ±0.0017

Difference within reported uncertainty; not counted as underperformance.

paper 0.3899 ±0.0017 Δ at pub 0.0127
64
ChebyNet
0.3917 ±0.0143
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.2555 ±0.0167
paper 0.2555 ±0.0167 Δ at pub 0.1362
68
GraphSAGE
0.3899 ±0.0085
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.3639 ±0.0035
paper 0.3639 ±0.0035 Δ at pub 0.0216 Δ today 0.0260
52
GPRGNN
—
0.3693 ± 0.0026
Accuracy (micro F1 per L1108) 0.3693 ± 0.0026
This paper
135
GCN
0.3690
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.2861 ±0.0039
paper 0.2861 ±0.0039 Δ at pub 0.0829
21
BernNet
—
0.3689 ± 0.0030
Accuracy (micro F1 per L1108) 0.3689 ± 0.0030
This paper
182
GAT
0.3605 ±0.0035
best reported
—
Accuracy (micro F1 per L1108) —
paper 0.3348 ±0.0035
paper 0.3348 ±0.0035 Δ at pub 0.0257
266
GIN
0.3410 ± 0.0030
—

Chameleon

Global leaderboard →
Non-default metric. This paper reports Accuracy (micro F1 per L1108); the dataset default is Accuracy. Values below use Accuracy (micro F1 per L1108) only.
#ModelAccuracy (micro F1 per L1108) ↑Paper
1
FE-GNN (C)
0.7333 ±0.0035
This paper

Squirrel

Global leaderboard →
Non-default metric. This paper reports Accuracy (micro F1 per L1108); the dataset default is Accuracy. Values below use Accuracy (micro F1 per L1108) only.
#ModelAccuracy (micro F1 per L1108) ↑Paper
1
FE-GNN (M)
0.6790 ±0.0023
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best at pub — reported value improved over the best known when published Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere