Simplifying approach to Node Classification in Graph Neural Networks

Sunil Kumar Maurya, Xin Liu, Tsuyoshi Murata

Main figure for Simplifying approach to Node Classification in Graph Neural Networks

Abstract

Graph Neural Networks (GNNs) have become one of the indispensable tools to learn from graph-structured data, and their usefulness has been shown in wide variety of tasks. In recent years, there have been tremendous improvements in architecture design, resulting in better performance on various prediction tasks. In general, these neural architectures combine node feature aggregation and feature transformation using learnable weight matrix in the same layer. This makes it challenging to analyze the importance of node features aggregated from various hops and the expressiveness of the neural network layers. As different graph datasets show varying levels of homophily and heterophily in features and class label distribution, it becomes essential to understand which features are important for the prediction tasks without any prior information. In this work, we decouple the node feature aggregation step and depth of graph neural network, and empirically analyze how different aggregated features play a role in prediction performance. We show that not all features generated via aggregation steps are useful, and often using these less informative features can be detrimental to the performance of the GNN model. Through our experiments, we show that learning certain subsets of these features can lead to better performance on wide variety of datasets. Based on our observations, we introduce several key design strategies for graph neural networks. More specifically, we propose to use softmax as a regularizer and "soft-selector" of features aggregated from neighbors at different hop distances; and L2-Normalization over GNN layers. Combining these techniques, we present a simple and shallow model, Feature Selection Graph Neural Network (FSGNN), and show empirically that the proposed model achieves comparable or even higher accuracy than state-of-the-art GNN models in nine benchmark datasets for the node classification task, with remarkable improvements up to 51.1\

Benchmark Results

Tested on 7 datasets 7 baseline values reported too low

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

Classic

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
0.9004
67
SoTA
0.8849
This paper
724
MLP
0.7768

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
34
MLP
0.9230 ±0.0070
53
GraphSAGE
0.9000 ±0.0365
76
FSGNN (Sub_feature) SUM
0.8891
This paper
80
FSGNN (Sub_feature) CAT
0.8864
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
0.9480 ±0.0380
3
RF-GCN
0.9429
22
GPRGNN
actual #22 vs paper #158 136 places worse
0.8189 ±0.0617
actual #22 vs paper #158 136 places worse
paper 0.8189 ±0.0617
paper 0.8189 ±0.0617 Δ at pub 0.2362 Δ today 0.0968
24
MLP
0.9136 ±0.0070
35
GCNII
actual #35 vs paper #218 183 places worse
0.8918 ±0.0396
best reported
actual #35 vs paper #218 183 places worse
paper 0.7649 ±0.0437
paper 0.7649 ±0.0437 Δ at pub 0.0381 Δ today 0.1269
47
FSGNN (Homo/Hetero) 3-hop
0.8730 ±0.0593
This paper
48
FSGNN (Homo/Hetero) 8-hop
0.8730 ±0.0453
This paper
56
FSGNN
0.8675
This paper
138
SAGE
0.8269
153
H2GCN-1
0.8216 ±0.0480
This paper
157
GraphSAGE
actual #157 vs paper #222 65 places worse
0.8196 ±0.0739
best reported
actual #157 vs paper #222 65 places worse
paper 0.7595 ±0.0501

Difference within reported uncertainty; not counted as underperformance.

paper 0.7595 ±0.0501 Δ today 0.0601
158
GAT
actual #158 vs paper #388 230 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #388 230 places worse
paper 0.5892 ±0.0332
160
WRGAT
0.8162 ±0.0390
This paper
170
GCN
actual #170 vs paper #417 247 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #417 247 places worse
paper 0.5703 ±0.0467
paper 0.5703 ±0.0467 Δ at pub 0.0232 Δ today 0.2379
183
MixHop
actual #183 vs paper #249 66 places worse
0.7950 ±0.0630
best reported
actual #183 vs paper #249 66 places worse
paper 0.7351 ±0.0634

Difference within reported uncertainty; not counted as underperformance.

paper 0.7351 ±0.0634 Δ at pub 0.0599
239
Cheby+JK
0.7459 ±0.0787
This paper
342
Geom-GCN
actual #342 vs paper #369 27 places worse
0.6412
best reported
actual #342 vs paper #369 27 places worse
paper 0.6081
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
42
MLP
0.4026 ±0.0108
52
GPRGNN
actual #52 vs paper #182 130 places worse
0.3604 ±0.0096
actual #52 vs paper #182 130 places worse
paper 0.3604 ±0.0096
paper 0.3604 ±0.0096 Δ at pub 0.0616 Δ today 0.0388
68
GraphSAGE
actual #68 vs paper #258 190 places worse
0.3899 ±0.0085
best reported
actual #68 vs paper #258 190 places worse
paper 0.3423 ±0.0099
paper 0.3423 ±0.0099 Δ today 0.0476
75
WRGAT
actual #75 vs paper #158 83 places worse
0.3860 ±0.0110
best reported
actual #75 vs paper #158 83 places worse
paper 0.3653 ±0.0077
paper 0.3653 ±0.0077 Δ today 0.0207
87
Geom-GCN
actual #87 vs paper #305 218 places worse
0.3810
best reported
actual #87 vs paper #305 218 places worse
paper 0.3163
paper 0.3163 Δ at pub 0.0647
135
GCN
actual #135 vs paper #342 207 places worse
0.3690
best reported
actual #135 vs paper #342 207 places worse
paper 0.3026 ±0.0079
paper 0.3026 ±0.0079 Δ at pub 0.0664
160
SoTA
0.3653
This paper
162
MixHop
actual #162 vs paper #297 135 places worse
0.3648 ±0.0120
best reported
actual #162 vs paper #297 135 places worse
paper 0.3222 ±0.0234
best at pub: Graph Pointer Neural Networks (AAAI 2021)
paper 0.3222 ±0.0234 Δ today 0.0426
182
GAT
actual #182 vs paper #417 235 places worse
0.3605 ±0.0035
best reported
actual #182 vs paper #417 235 places worse
paper 0.2628 ±0.0173
best at pub: Graph Pointer Neural Networks (AAAI 2021)
paper 0.2628 ±0.0173 Δ at pub 0.0346 Δ today 0.0977
190
H2GCN-1
actual #190 vs paper #192 2 places worse
0.3594 ±0.0130
best reported
actual #190 vs paper #192 2 places worse
paper 0.3586 ±0.0103

Difference within reported uncertainty; not counted as underperformance.

paper 0.3586 ±0.0103 Δ today 0.0008
199
SUM (Sub_feature)
0.3567
This paper
202
CAT (Sub_feature)
0.3563
This paper
205
FSGNN (Homo/Hetero) 8-hop
0.3562 ±0.0087
This paper
222
FSGNN (Homo/Hetero) 3-hop
0.3538 ±0.0081
This paper
223
X
0.3532
This paper
227
Cheby+JK
0.3514 ±0.0137
This paper
266
GIN
0.3410 ±0.0030
368
(A+I)X
0.2922
This paper
398
(A+I)^2X
0.2795
This paper
417
(A+I)^3X
0.2643
This paper
425
AX
0.2547
This paper
429
A^2X
0.2538
This paper
432
A^3X
0.2527
This paper
#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
actual #3 vs paper #167 164 places worse
0.8560
best reported
actual #3 vs paper #167 164 places worse
paper 0.5469 ±0.0195
paper 0.5469 ±0.0195 Δ at pub 0.1031 Δ today 0.3091
21
FSGNN (Homo/Hetero) 3-hop
0.7893 ±0.0103
This paper
33
FSGNN (Homo/Hetero) 8-hop
0.7394 ±0.0202
This paper
52
GCN
actual #52 vs paper #138 86 places worse
0.7033
best reported
actual #52 vs paper #138 86 places worse
paper 0.5982 ±0.0258
paper 0.5982 ±0.0258 Δ at pub 0.0778 Δ today 0.1051
72
GPRGNN
actual #72 vs paper #79 7 places worse
0.6748 ±0.0040
best reported
actual #72 vs paper #79 7 places worse
paper 0.6647 ±0.0247

Difference within reported uncertainty; not counted as underperformance.

paper 0.6647 ±0.0247 Δ today 0.0101
80
SoTA
0.6647
This paper
91
WRGAT
0.6524 ±0.0087
This paper
103
GCNII
actual #103 vs paper #113 10 places worse
0.6386 ±0.0304
best reported
actual #103 vs paper #113 10 places worse
paper 0.6248 ±0.0274

Difference within reported uncertainty; not counted as underperformance.

paper 0.6248 ±0.0274 Δ today 0.0138
104
Cheby+JK
0.6379 ±0.0227
This paper
108
SAGE
0.6340 ±0.0300
115
GraphSAGE
actual #115 vs paper #143 28 places worse
0.6215 ±0.0042
best reported
actual #115 vs paper #143 28 places worse
paper 0.5873 ±0.0168
paper 0.5873 ±0.0168 Δ today 0.0342
124
Geom-GCN
0.6090
This paper
129
MixHop
0.6050 ±0.0253
This paper
156
H2GCN-1
0.5711 ±0.0158
This paper
169
MLP
0.5429
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
11
FSGNN
0.7416
This paper
46
GCN
actual #46 vs paper #197 151 places worse
0.6067
best reported
actual #46 vs paper #197 151 places worse
paper 0.3689 ±0.0134
paper 0.3689 ±0.0134 Δ at pub 0.1801 Δ today 0.2378
67
GAT
actual #67 vs paper #240 173 places worse
0.5630 ±0.0220
best reported
actual #67 vs paper #240 173 places worse
paper 0.3062 ±0.0211
paper 0.3062 ±0.0211 Δ at pub 0.2068 Δ today 0.2568
76
GPRGNN
actual #76 vs paper #94 18 places worse
0.5435 ±0.0087
best reported
actual #76 vs paper #94 18 places worse
paper 0.4903 ±0.0128
paper 0.4903 ±0.0128 Δ today 0.0532
95
SoTA
0.4903
This paper
96
WRGAT
0.4885 ±0.0078
This paper
119
Cheby+JK
0.4503 ±0.0173
This paper
120
SAGE
0.4460 ±0.0130
127
MixHop
0.4380 ±0.0148
This paper
128
GraphSAGE
actual #128 vs paper #150 22 places worse
0.4378 ±0.0190
best reported
actual #128 vs paper #150 22 places worse
paper 0.4161 ±0.0074

Difference within reported uncertainty; not counted as underperformance.

paper 0.4161 ±0.0074 Δ today 0.0217
172
MLP
0.3930 ±0.0079
179
Geom-GCN
actual #179 vs paper #181 2 places worse
0.3814
actual #179 vs paper #181 2 places worse
paper 0.3814
paper 0.3814 Δ at pub 0.0004
203
H2GCN-1
0.3642 ±0.0189
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