Geometry Contrastive Learning on Heterogeneous Graphs

Shichao Zhu, Chuan Zhou, Anfeng Cheng, Shirui Pan, Shuaiqiang Wang, Dawei Yin, Bin Wang

Main figure for Geometry Contrastive Learning on Heterogeneous Graphs

Abstract

Self-supervised learning (especially contrastive learning) methods on heterogeneous graphs can effectively get rid of the dependence on supervisory data. Meanwhile, most existing representation learning methods embed the heterogeneous graphs into a single geometric space, either Euclidean or hyperbolic. This kind of single geometric view is usually not enough to observe the complete picture of heterogeneous graphs due to their rich semantics and complex structures. Under these observations, this paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL), to better represent the heterogeneous graphs when supervisory data is unavailable. GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures, which is expected to bring in more benefits for downstream tasks. GCL maximizes the mutual information between two geometric views by contrasting representations at both local-local and local-global semantic levels. Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines, including both unsupervised methods and supervised methods, on three tasks—node classification, node clustering and similarity search.

Proposed method: GCL

Benchmark Results

Tested on 4 datasets 14 baseline values reported too low Non-standard metric on 1 dataset

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

Heterogeneous Graph Benchmarks

#ModelMicro-F1 ↑Paper
1
LMSPS
0.9566 ±0.0020
2
PSHGCN
0.9561 ±0.0012
3
RpHGNN
0.9555 ±0.0029
21
GCN
actual #21 vs paper #171 150 places worse
0.9460 ±0.0031
best reported
actual #21 vs paper #171 150 places worse
paper 0.6864 ±0.0050
23
GAT
actual #23 vs paper #165 142 places worse
0.9448 ±0.0022
best reported
actual #23 vs paper #165 142 places worse
paper 0.7135 ±0.0051
best at pub: Heterogeneous Graph Benchmarks (KDD 2021)
paper 0.7135 ±0.0051 Δ at pub 0.2204 Δ today 0.2313
37
HAN
actual #37 vs paper #167 130 places worse
0.9369
best reported
actual #37 vs paper #167 130 places worse
paper 0.7075 ±0.0089
44
DMGI
actual #44 vs paper #141 97 places worse
0.7850 ±0.0105
actual #44 vs paper #141 97 places worse
paper 0.7850 ±0.0105
prev best: Implicit Graph Neural Networks (NeurIPS 2020)
paper 0.7850 ±0.0105 Δ at pub 0.0190 Δ today 0.1481
46
GraphSAGE
0.9306 ±0.0047
50
MVGRL
actual #50 vs paper #160 110 places worse
0.9289
best reported
actual #50 vs paper #160 110 places worse
paper 0.7308 ±0.0196
paper 0.7308 ±0.0196 Δ at pub 0.1981
52
Node2Vec
actual #52 vs paper #185 133 places worse
0.9282
best reported
actual #52 vs paper #185 133 places worse
paper 0.5469 ±0.0081
paper 0.5469 ±0.0081 Δ at pub 0.3813
61
HDGI
actual #61 vs paper #144 83 places worse
0.9233
best reported
actual #61 vs paper #144 83 places worse
paper 0.7795 ±0.0082
paper 0.7795 ±0.0082 Δ at pub 0.1438
74
GRACE
actual #74 vs paper #166 92 places worse
0.7113 ±0.0132
actual #74 vs paper #166 92 places worse
paper 0.7113 ±0.0132
paper 0.7113 ±0.0132 Δ at pub 0.0225 Δ today 0.2015
79
DGI
actual #79 vs paper #159 80 places worse
0.7378 ±0.0151
actual #79 vs paper #159 80 places worse
paper 0.7378 ±0.0151
prev best: Implicit Graph Neural Networks (NeurIPS 2020)

Improvement within reported uncertainty; not highlighted.

paper 0.7378 ±0.0151 Δ at pub 0.0178 Δ today 0.1638
81
DeepWalk
actual #81 vs paper #185 104 places worse
0.9012 ±0.0045
best reported
actual #81 vs paper #185 104 places worse
paper 0.5367 ±0.0070
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)
paper 0.5367 ±0.0070 Δ at pub 0.0003 Δ today 0.3645
89
R-GCN
actual #89 vs paper #169 80 places worse
0.8700 ±0.0070
best reported
actual #89 vs paper #169 80 places worse
paper 0.6901 ±0.0148
paper 0.6901 ±0.0148 Δ today 0.1799
136
GCL
0.8027 ±0.0136
This paper
166
MGCN
actual #166 vs paper #166
0.7130
best reported
actual #166 vs paper #166
paper 0.7129 ±0.0093
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7129 ±0.0093 Δ at pub 0.0001
176
MLP
0.6447 ±0.0136
187
Raw features
0.5170 ±0.0069
This paper
#ModelMicro-F1 ↑Paper
1
LMSPS
0.9469 ±0.0036
2
PSHGCN
0.9427 ±0.0023
3
SlotGAT
0.9406 ±0.0022
19
GAT
actual #19 vs paper #94 75 places worse
0.9273
best reported
actual #19 vs paper #94 75 places worse
paper 0.8550 ±0.0054
paper 0.8550 ±0.0054 Δ at pub 0.0723
29
GCN
actual #29 vs paper #95 66 places worse
0.9229
best reported
actual #29 vs paper #95 66 places worse
paper 0.8482 ±0.0056
paper 0.8482 ±0.0056 Δ at pub 0.0747
43
HAN
actual #43 vs paper #66 23 places worse
0.9147 ±0.0022
best reported
actual #43 vs paper #66 23 places worse
paper 0.8924 ±0.0059
best at pub: Heterogeneous Graph Benchmarks (KDD 2021)
paper 0.8924 ±0.0059 Δ at pub 0.0155 Δ today 0.0223
49
GIN
0.9092
56
GCL
0.9051 ±0.0081
This paper
64
DMGI
actual #64 vs paper #79 15 places worse
0.8980 ±0.0010
best reported
actual #64 vs paper #79 15 places worse
paper 0.8800 ±0.0131
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8800 ±0.0131 Δ at pub 0.0180 Δ today 0.0180
66
HDGI
0.8930 ±0.0142
This paper
74
DGI
actual #74 vs paper #83 9 places worse
0.8844 ±0.0030
best reported
actual #74 vs paper #83 9 places worse
paper 0.8773 ±0.0170
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8773 ±0.0170 Δ at pub 0.0037 Δ today 0.0071
79
MVGRL
actual #79 vs paper #79
0.8803 ±0.0138
actual #79 vs paper #79
paper 0.8803 ±0.0138
paper 0.8803 ±0.0138 Δ at pub 0.0425
81
MGCN
actual #81 vs paper #91 10 places worse
0.8788 ±0.0054
best reported
actual #81 vs paper #91 10 places worse
paper 0.8606 ±0.0045
paper 0.8606 ±0.0045 Δ at pub 0.0182
84
GRACE
actual #84 vs paper #96 12 places worse
0.8764 ±0.0031
best reported
actual #84 vs paper #96 12 places worse
paper 0.8439 ±0.0147
paper 0.8439 ±0.0147 Δ at pub 0.0154 Δ today 0.0325
91
R-GCN
0.8608 ±0.0025
This paper
100
DeepWalk
actual #100 vs paper #104 4 places worse
0.7489 ±0.0053
actual #100 vs paper #104 4 places worse
paper 0.7489 ±0.0053
prev best: Implicit Graph Neural Networks (NeurIPS 2020)

Improvement within reported uncertainty; not highlighted.

paper 0.7489 ±0.0053 Δ at pub 0.0009 Δ today 0.0689
105
Node2Vec
0.7488 ±0.0056
This paper
108
Raw features
0.7213 ±0.0045
This paper
109
MLP
0.7102 ±0.0221
#ModelMicro-F1 ↑Paper
1
ELLA
0.7930 ±0.0010
2
MHGCN
0.7820 ±0.0138
3
PSHGCN
0.7446 ±0.0032
14
GCN
actual #14 vs paper #48 34 places worse
0.6813 ±0.0083
best reported
actual #14 vs paper #48 34 places worse
paper 0.6199 ±0.0054
best at pub: Heterogeneous Graph Benchmarks (KDD 2021)
paper 0.6199 ±0.0054 Δ at pub 0.0283 Δ today 0.0614
15
GAT
actual #15 vs paper #48 33 places worse
0.6808 ±0.0049
best reported
actual #15 vs paper #48 33 places worse
paper 0.6112 ±0.0046
best at pub: Heterogeneous Graph Benchmarks (KDD 2021)
paper 0.6112 ±0.0046 Δ at pub 0.0374 Δ today 0.0696
18
HAN
actual #18 vs paper #55 37 places worse
0.6769 ±0.0064
best reported
actual #18 vs paper #55 37 places worse
paper 0.6030 ±0.0047
best at pub: Heterogeneous Graph Benchmarks (KDD 2021)
paper 0.6030 ±0.0047 Δ at pub 0.0433 Δ today 0.0739
32
GCL
0.6514 ±0.0047
This paper
33
DMGI
actual #33 vs paper #42 9 places worse
0.6480
best reported
actual #33 vs paper #42 9 places worse
paper 0.6316 ±0.0122
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)

Difference within reported uncertainty; not counted as underperformance.

paper 0.6316 ±0.0122 Δ at pub 0.0164 Δ today 0.0164
37
GRACE
0.6407 ±0.0080
This paper
43
MGCN
actual #43 vs paper #43
0.6308 ±0.0038
actual #43 vs paper #43
paper 0.6308 ±0.0038
prev best: Implicit Graph Neural Networks (NeurIPS 2020)

Improvement within reported uncertainty; not highlighted.

paper 0.6308 ±0.0038 Δ at pub 0.0008
44
GraphSAGE
0.6276
47
R-GCN
0.6214 ±0.0066
This paper
51
HDGI
0.6083 ±0.0089
This paper
54
DGI
actual #54 vs paper #61 7 places worse
0.6060
best reported
actual #54 vs paper #61 7 places worse
paper 0.5839 ±0.0059
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)
paper 0.5839 ±0.0059 Δ at pub 0.0221
59
MVGRL
0.5930 ±0.0093
This paper
65
Raw features
0.5706 ±0.0070
This paper
68
DeepWalk
actual #68 vs paper #75 7 places worse
0.5636 ±0.0033
best reported
actual #68 vs paper #75 7 places worse
paper 0.5460 ±0.0052
best at pub: Implicit Graph Neural Networks (NeurIPS 2020)
paper 0.5460 ±0.0052 Δ at pub 0.0040 Δ today 0.0176
74
MLP
0.5514
75
Node2Vec
0.5476 ±0.0063
This paper

Other Graph Benchmarks

Amazon2M

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

Sorted by Macro-F1. Highlighted rows are from other papers.

#ModelMacro-F1 ↑Paper
1
GCL
0.7650 ±0.0122
This paper
2
DMGI
0.7469 ±0.0112
This paper
3
Raw features
0.7030 ±0.0075
This paper
4
GRACE
0.6707 ±0.0139
This paper
5
DeepWalk
0.6631 ±0.0079
This paper
6
Node2Vec
0.6621 ±0.0077
This paper
7
MGCN
0.6592 ±0.0046
This paper
8
R-GCN
0.6401 ±0.0120
This paper
9
GCN
0.6360 ±0.0095
This paper
10
HAN
0.5343 ±0.0080
This paper
11
GAT
0.5193 ±0.0036
This paper
12
HDGI
0.4293 ±0.0184
This paper
13
DGI
0.4028 ±0.0141
This paper
14
MVGRL
0.3838 ±0.0135
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