On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs

Hejie Cui, Zijie Lu, Pan Li, Carl Yang

Main figure for On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs

Abstract

Graph neural networks (GNNs) have been widely used in various graph-related problems such as node classification and graph classification, where the superior performance is mainly established when natural node features are available. However, it is not well understood how GNNs work without natural node features, especially regarding the various ways to construct artificial ones. In this paper, we point out the two types of artificial node features, i.e., positional and structural node features, and provide insights on why each of them is more appropriate for certain tasks, i.e., positional node classification, structural node classification, and graph classification. Extensive experimental results on 10 benchmark datasets validate our insights, thus leading to a practical guideline on the choices between different artificial node features for GNNs on non-attributed graphs. The code is available at.

Proposed method: Degree

Benchmark Results

Tested on 1 dataset 1 baseline value reported too low

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

TU Dortmund

#ModelAccuracy ↑Paper
1
MSH-GNN
0.9910 ±0.0030
2
ID-GNN+BEC
0.9830 ±0.0360
3
SupCosine
0.9830 ±0.0250
39
GIN
0.9330 ±0.0290
403
MLP
0.8660 ±0.0495
476
Degree
0.8440 ±0.0770
This paper
521
real feat.
0.8300 ±0.0630
This paper
535
Random
actual #535 vs paper #771 236 places worse
0.8270 ±0.0680
best reported
actual #535 vs paper #771 236 places worse
paper 0.6690 ±0.0710
paper 0.6690 ±0.0710 Δ at pub 0.1580
620
shared
0.7990 ±0.0670
This paper
675
PageRank
0.7730 ±0.0760
This paper
775
one-hot
0.6580 ±0.0700
This paper
778
eigen
0.6540 ±0.0770
This paper
781
DeepWalk
0.6510 ±0.0830
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)