Clarify Confused Nodes via Separated Learning

Jiajun Zhou, Sheng Gong, Chenxuan Xie, Shanqing Yu, Qi Xuan, Xiaoniu Yang

Main figure for Clarify Confused Nodes via Separated Learning

Abstract

Graph neural networks (GNNs) have achieved remarkable advances in graph-oriented tasks. However, real-world graphs invariably contain a certain proportion of heterophilous nodes, challenging the homophily assumption of traditional GNNs and hindering their performance. Most existing studies continue to design generic models with shared weights between heterophilous and homophilous nodes. Despite the incorporation of high-order messages or multi-channel architectures, these efforts often fall short. A minority of studies attempt to train different node groups separately but suffer from inappropriate separation metrics and low efficiency. In this paper, we first propose a new metric, termed Neighborhood Confusion (NC), to facilitate a more reliable separation of nodes. We observe that node groups with different levels of NC values exhibit certain differences in intra-group accuracy and visualized embeddings. These pave the way for Neighborhood Confusion-guided Graph Convolutional Network (NCGCN), in which nodes are grouped by their NC values and accept intra-group weight sharing and message passing. Extensive experiments on both homophilous and heterophilous benchmarks demonstrate that our framework can effectively separate nodes and yield significant performance improvement compared to the latest methods. The source code is available in.

Benchmark Results

Tested on 4 datasets 4 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 #89 87 places worse
0.9421 ±0.0057
actual #2 vs paper #89 87 places worse
paper 0.9421 ±0.0057
3
GAT+T
0.9660 ±0.0007
7
SAGE
actual #7 vs paper #174 167 places worse
0.9643 ±0.0027
best reported
actual #7 vs paper #174 167 places worse
paper 0.9332 ±0.0045
8
GCN
actual #8 vs paper #103 95 places worse
0.9394 ±0.0047
actual #8 vs paper #103 95 places worse
paper 0.9394 ±0.0047
33
GPRGNN
actual #33 vs paper #101 68 places worse
0.9397 ±0.0067
actual #33 vs paper #101 68 places worse
paper 0.9397 ±0.0067

Improvement within reported uncertainty; not highlighted.

paper 0.9397 ±0.0067 Δ at pub 0.0010 Δ today 0.0152
34
H2GCN
0.9548 ±0.0043
This paper
48
GloGNN
actual #48 vs paper #294 246 places worse
0.9517 ±0.0029
best reported
actual #48 vs paper #294 246 places worse
paper 0.9241 ±0.0072
paper 0.9241 ±0.0072 Δ today 0.0276
56
GraphSAGE
0.9508 ±0.0026
58
ACM-GCN
0.9504 ±0.0044
This paper
66
FAGCN
actual #66 vs paper #66
0.9489 ±0.0048
actual #66 vs paper #66
paper 0.9489 ±0.0048
paper 0.9489 ±0.0048 Δ at pub 0.0122
319
WRGAT
0.9223 ±0.0064
This paper
390
MLP
actual #390 vs paper #390
0.9128 ±0.0063
actual #390 vs paper #390
paper 0.9128 ±0.0063
paper 0.9128 ±0.0063 Δ at pub 0.0311
405
HOG
0.9088 ±0.0068
This paper
412
SNGNN
0.9079 ±0.0259
This paper
431
CPGNN
0.9049 ±0.0243
This paper
526
GBKSage
0.8161 ±0.0805
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #120 118 places worse
0.8972 ±0.0043
actual #2 vs paper #120 118 places worse
paper 0.8972 ±0.0043
paper 0.8972 ±0.0043 Δ at pub 0.0187 Δ today 0.0440
3
GAT
actual #3 vs paper #119 116 places worse
0.8974 ±0.0047
actual #3 vs paper #119 116 places worse
paper 0.8974 ±0.0047
8
SAGE
actual #8 vs paper #100 92 places worse
0.9001 ±0.0077
actual #8 vs paper #100 92 places worse
paper 0.9001 ±0.0077
46
GraphSAGE
0.9120 ±0.0029
72
GPRGNN
actual #72 vs paper #212 140 places worse
0.8792 ±0.0196
actual #72 vs paper #212 140 places worse
paper 0.8792 ±0.0196

Improvement within reported uncertainty; not highlighted.

paper 0.8792 ±0.0196 Δ at pub 0.0072
80
ACM-GCN
0.9031 ±0.0039
This paper
114
H2GCN
actual #114 vs paper #125 11 places worse
0.8986 ±0.0022
best reported
actual #114 vs paper #125 11 places worse
paper 0.8968 ±0.0102

Difference within reported uncertainty; not counted as underperformance.

paper 0.8968 ±0.0102 Δ today 0.0018
126
FAGCN
actual #126 vs paper #228 102 places worse
0.8968 ±0.0097
best reported
actual #126 vs paper #228 102 places worse
paper 0.8761 ±0.0117
paper 0.8761 ±0.0117 Δ at pub 0.0207
152
GloGNN
actual #152 vs paper #286 134 places worse
0.8912 ±0.0033
best reported
actual #152 vs paper #286 134 places worse
paper 0.8605 ±0.0171
paper 0.8605 ±0.0171 Δ today 0.0307
285
WRGAT
0.8613 ±0.0076
This paper
320
MLP
actual #320 vs paper #337 17 places worse
0.8435 ±0.0102
actual #320 vs paper #337 17 places worse
paper 0.8435 ±0.0102
paper 0.8435 ±0.0102 Δ at pub 0.0257
369
CPGNN
0.8350 ±0.0223
This paper
403
HOG
0.8207 ±0.0131
This paper
416
GBKSage
0.8120 ±0.0562
This paper
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
0.9796 ±0.0081
6
GAT
actual #6 vs paper #38 32 places worse
0.9663 ±0.0025
actual #6 vs paper #38 32 places worse
paper 0.9663 ±0.0025
paper 0.9663 ±0.0025 Δ at pub 0.0043 Δ today 0.0119
7
GPRGNN
actual #7 vs paper #7
0.9777 ±0.0015
actual #7 vs paper #7
paper 0.9777 ±0.0015
paper 0.9777 ±0.0015 Δ at pub 0.0402
9
GCN
actual #9 vs paper #47 38 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #47 38 places worse
paper 0.9631 ±0.0015
paper 0.9631 ±0.0015 Δ at pub 0.0019 Δ today 0.0143
11
H2GCN
0.9764 ±0.0050
This paper
12
CPGNN
0.9761 ±0.0048
This paper
15
GloGNN
0.9754 ±0.0053
This paper
17
SAGE
0.9739 ±0.0018
This paper
19
FAGCN
0.9737 ±0.0033
This paper
30
ACM-GCN
0.9709 ±0.0020
This paper
43
GraphSAGE
0.9649 ±0.0006
58
MLP
actual #58 vs paper #95 37 places worse
0.9563 ±0.0024
actual #58 vs paper #95 37 places worse
paper 0.9563 ±0.0024
paper 0.9563 ±0.0024 Δ at pub 0.0072

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
DC-GNN
0.8669 ±0.0022
2
M2M-GNN
0.8594 ±0.0040
3
GloGNN
actual #3 vs paper #25 22 places worse
0.8574 ±0.0042
best reported
actual #3 vs paper #25 22 places worse
paper 0.8307 ±0.0135
paper 0.8307 ±0.0135 Δ at pub 0.0253 Δ today 0.0267
13
GPRGNN
0.8455 ±0.0054
This paper
24
H2GCN
actual #24 vs paper #24
0.8320 ±0.0055
actual #24 vs paper #24
paper 0.8320 ±0.0055
paper 0.8320 ±0.0055 Δ at pub 0.0166
26
ACM-GCN
actual #26 vs paper #26
0.8298 ±0.0063
actual #26 vs paper #26
paper 0.8298 ±0.0063

Improvement within reported uncertainty; not highlighted.

paper 0.8298 ±0.0063 Δ at pub 0.0030
29
GIN
0.8268 ±0.0032
31
GCN
actual #31 vs paper #50 19 places worse
0.8247 ±0.0027
best reported
actual #31 vs paper #50 19 places worse
paper 0.7655 ±0.0057
paper 0.7655 ±0.0057 Δ at pub 0.0592 Δ today 0.0592
36
GAT
actual #36 vs paper #44 8 places worse
0.8153 ±0.0055
best reported
actual #36 vs paper #44 8 places worse
paper 0.7768 ±0.0237
paper 0.7768 ±0.0237 Δ at pub 0.0377 Δ today 0.0385
46
FAGCN
0.7697 ±0.0069
This paper
51
MLP
actual #51 vs paper #51
0.7534 ±0.0064
actual #51 vs paper #51
paper 0.7534 ±0.0064
paper 0.7534 ±0.0064 Δ at pub 0.0173
SOTA performance (not significantly different from the best) 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