NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification

Rui Yang, Wenrui Dai, Chenglin Li, Junni Zou, H. Xiong

Main figure for NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification

Abstract

Message passing has evolved as an effective tool for designing Graph Neural Networks (GNNs). However, most existing methods for message passing simply sum or average all the neighboring features to update node representations. They are restricted by two problems, i.e., (i) lack of interpretability to identify node features significant to the prediction of GNNs, and (ii) feature over-mixing that leads to the over-smoothing issue in capturing long-range dependencies and inability to handle graphs under heterophily or low homophily. In this paper, we propose a Node-level Capsule Graph Neural Network (NCGNN) to address these problems with an improved message passing scheme. Specifically, NCGNN represents nodes as groups of node-level capsules, in which each capsule extracts distinctive features of its corresponding node. For each node-level capsule, a novel dynamic routing procedure is developed to adaptively select appropriate capsules for aggregation from a subgraph identified by the designed graph filter. NCGNN aggregates only the advantageous capsules and restrains irrelevant messages to avoid over-mixing features of interacting nodes. Therefore, it can relieve the over-smoothing issue and learn effective node representations over graphs with homophily or heterophily. Furthermore, our proposed message passing scheme is inherently interpretable and exempt from complex post-hoc explanations, as the graph filter and the dynamic routing procedure identify a subset of node features that are most significant to the model prediction from the extracted subgraph. Extensive experiments on synthetic as well as real-world graphs demonstrate that NCGNN can well address the over-smoothing issue and produce better node representations for semisupervised node classification. It outperforms the state of the arts under both homophily and heterophily.

Benchmark Results

Tested on 5 datasets 8 baseline values reported too low

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 #467 465 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #467 465 places worse
paper 0.8936
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #323 315 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #323 315 places worse
paper 0.9221
21
APPNP
actual #21 vs paper #344 323 places worse
0.9196
actual #21 vs paper #344 323 places worse
paper 0.9196
50
SGC
actual #50 vs paper #430 380 places worse
0.9049
actual #50 vs paper #430 380 places worse
paper 0.9049
87
GCNII
actual #87 vs paper #453 366 places worse
0.9430 ±0.0020
best reported
actual #87 vs paper #453 366 places worse
paper 0.8988
paper 0.8988 Δ today 0.0442
214
NCGNN-A
0.9308
This paper
215
Scattering GCN
actual #215 vs paper #526 311 places worse
0.9307 ±0.0042
best reported
actual #215 vs paper #526 311 places worse
paper 0.8151
paper 0.8151 Δ today 0.1156
233
NCGNN-D
0.9286
This paper
260
DAGNN
0.9269
This paper
322
AdaEdge
0.9222
This paper
324
DropEdge
0.9221
This paper
349
JK-Net
actual #349 vs paper #359 10 places worse
0.9190 ±0.0070
best reported
actual #349 vs paper #359 10 places worse
paper 0.9176

Difference within reported uncertainty; not counted as underperformance.

paper 0.9176 Δ today 0.0014
390
MLP
0.9128 ±0.0063
424
BBGDC
0.9059
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #390 388 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #390 388 places worse
paper 0.8245
paper 0.8245 Δ at pub 0.0540 Δ today 0.1167
3
GAT
actual #3 vs paper #387 384 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #387 384 places worse
paper 0.8280
8
SAGE
0.9351 ±0.0006
52
GCNII
actual #52 vs paper #417 365 places worse
0.9104 ±0.0041
best reported
actual #52 vs paper #417 365 places worse
paper 0.8113
paper 0.8113 Δ today 0.0991
58
APPNP
actual #58 vs paper #413 355 places worse
0.9093 ±0.0018
best reported
actual #58 vs paper #413 355 places worse
paper 0.8139
82
SGC
actual #82 vs paper #375 293 places worse
0.8338
actual #82 vs paper #375 293 places worse
paper 0.8338

Improvement within reported uncertainty; not highlighted.

paper 0.8338 Δ at pub 0.0158 Δ today 0.0684
168
Scattering GCN
actual #168 vs paper #477 309 places worse
0.8883 ±0.0044
best reported
actual #168 vs paper #477 309 places worse
paper 0.6869
paper 0.6869 Δ today 0.2014
204
NCGNN-A
0.8812
This paper
206
NCGNN-D
0.8811
This paper
320
MLP
0.8463
324
DAGNN
actual #324 vs paper #387 63 places worse
0.8450 ±0.0120
best reported
actual #324 vs paper #387 63 places worse
paper 0.8278

Difference within reported uncertainty; not counted as underperformance.

paper 0.8278 Δ today 0.0172
398
DropEdge
0.8230
This paper
399
AdaEdge
0.8218
This paper
404
JK-Net
actual #404 vs paper #429 25 places worse
0.8200 ±0.0060
best reported
actual #404 vs paper #429 25 places worse
paper 0.7993

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
actual #34 vs paper #207 173 places worse
0.8189
actual #34 vs paper #207 173 places worse
paper 0.8189

Improvement within reported uncertainty; not highlighted.

paper 0.8189 Δ at pub 0.0059 Δ today 0.1041
53
GraphSAGE
0.9000 ±0.0365
70
GCNII
actual #70 vs paper #314 244 places worse
0.8918 ±0.0443
best reported
actual #70 vs paper #314 244 places worse
paper 0.7546
paper 0.7546 Δ today 0.1372
150
H2GCN-1
0.8486
This paper
163
NCGNN-A
0.8443
This paper
203
H2GCN-2
0.8216
This paper
211
GAT
actual #211 vs paper #533 322 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #533 322 places worse
paper 0.5838
best at pub: Heterophilic Graphs (ICLR 2020)
paper 0.5838 Δ today 0.2324
257
GCN
actual #257 vs paper #513 256 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #513 256 places worse
paper 0.5946
best today: Graph Wave Networks (WWW 2025)
paper 0.5946 Δ at pub 0.0164 Δ today 0.1987
348
Geom-GCN-S
actual #348 vs paper #508 160 places worse
0.7350
best reported
actual #348 vs paper #508 160 places worse
paper 0.5973
paper 0.5973 Δ at pub 0.1377
386
DAGNN
actual #386 vs paper #518 132 places worse
0.7027 ±0.0493
best reported
actual #386 vs paper #518 132 places worse
paper 0.5935
416
Geom-GCN-P
0.6757
This paper
548
Geom-GCN-I
0.5758
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
0.9480 ±0.0380
3
RF-GCN
0.9429
24
MLP
actual #24 vs paper #166 142 places worse
0.9136 ±0.0070
best reported
actual #24 vs paper #166 142 places worse
paper 0.8108
paper 0.8108 Δ at pub 0.0052 Δ today 0.1028
35
GCNII
actual #35 vs paper #197 162 places worse
0.8918 ±0.0396
best reported
actual #35 vs paper #197 162 places worse
paper 0.7811
paper 0.7811 Δ today 0.1107
118
NCGNN-A
0.8379
This paper
138
SAGE
0.8269
153
H2GCN-1
0.8216
This paper
154
H2GCN-2
0.8216
This paper
158
GAT
actual #158 vs paper #388 230 places worse
0.5892
actual #158 vs paper #388 230 places worse
paper 0.5892
170
GCN
actual #170 vs paper #417 247 places worse
0.5703
actual #170 vs paper #417 247 places worse
paper 0.5703
226
Geom-GCN-S
actual #226 vs paper #426 200 places worse
0.7540
best reported
actual #226 vs paper #426 200 places worse
paper 0.5568
paper 0.5568 Δ at pub 0.1972
250
DAGNN
actual #250 vs paper #377 127 places worse
0.7351 ±0.0718
best reported
actual #250 vs paper #377 127 places worse
paper 0.5989
370
Geom-GCN-P
0.6081
This paper
419
Geom-GCN-I
0.5676
This paper
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
38
GCNII
actual #38 vs paper #273 235 places worse
0.4082 ±0.0179
best reported
actual #38 vs paper #273 235 places worse
paper 0.3385
paper 0.3385 Δ today 0.0697
42
MLP
actual #42 vs paper #195 153 places worse
0.3576
actual #42 vs paper #195 153 places worse
paper 0.3576

Improvement within reported uncertainty; not highlighted.

paper 0.3576 Δ at pub 0.0066 Δ today 0.0450
68
GraphSAGE
0.3899 ±0.0085
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
paper 0.3026 Δ at pub 0.0004 Δ today 0.0664
140
NCGNN
0.3684
This paper
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
paper 0.2628 Δ at pub 0.0312 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

Difference within reported uncertainty; not counted as underperformance.

paper 0.3586 Δ today 0.0008
204
H2GCN-2
0.3562
This paper
211
DAGNN
actual #211 vs paper #277 66 places worse
0.3551 ±0.0110
best reported
actual #211 vs paper #277 66 places worse
paper 0.3368
248
Geom-GCN-S
actual #248 vs paper #356 108 places worse
0.3460
best reported
actual #248 vs paper #356 108 places worse
paper 0.2983
paper 0.2983 Δ at pub 0.0477
306
Geom-GCN-P
actual #306 vs paper #317 11 places worse
0.3163
best reported
actual #306 vs paper #317 11 places worse
paper 0.3128
best at pub: Heterophilic Graphs (ICLR 2020)
paper 0.3128 Δ at pub 0.0035
371
Geom-GCN-I
actual #371 vs paper #382 11 places worse
0.2909
best reported
actual #371 vs paper #382 11 places worse
paper 0.2865
best at pub: Heterophilic Graphs (ICLR 2020)
paper 0.2865 Δ at pub 0.0044
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) Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere