1 Introduction
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We propose a new framework that combines AL with ST to reduce labeling cost and boost the performance of GNNs.
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We introduce a simple but effective strategy to obtain reliable pseudo-labels in self-training.
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We confirm through experimentation on several benchmark datasets the effectiveness of the proposed approach.
2 Related work
2.1 Graph Neural Networks
2.2 Active learning
2.3 Self-training GNNs
2.4 Hybrid methods
3 Preliminaries
3.1 Notation
3.2 Problem formulation
4 Methodology
4.1 Active learning
4.2 Self-training with confident nodes
4.3 Label prediction
5 Experiments
5.1 Evaluation protocol
Dataset | \(\mid V \mid\) | \(\mid E \mid\) | \(\mid {c} \mid\) | R |
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Cora | 2708 | 10,556 | 7 | 1433 |
Citeseer | 3327 | 9104 | 6 | 3703 |
Pubmed | 19,717 | 88,648 | 3 | 500 |
ogbn-arxiv | 169,343 | 1,166,243 | 40 | 128 |
Hyper-parameter | Values |
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Learning rate | {1e\(-\)2, 1e\(-\)3, 1e\(-\)4} |
Dropout | {0, 0.3, 0.5, 0.8} |
Layers | {2, 4, 6} |
Heads | {2, 4} |
Hidden dimension | {16, 32, 64, 128} |
5.2 Ablation study
5.2.1 Variants of STAL
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GCN: A vanilla GCN trained with the full set of labels.
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ST: A GCN model that utilizes the self-training strategy only.
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AL\(_{\epsilon }\): An AL model that utilizes the uncertainty-based entropy strategy.
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AL\(_{QbC}\): An AL model that utilizes the QbC entropy-based strategy, with a committee of five models.
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AL\(_{AGE}\): An AL model that utilizes the AGE strategy only.
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STAL\(_{\epsilon }\): STAL with the entropy strategy.
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STAL\(_{QbC}\): STAL with the QbC entropy-based strategy, using a committee of five models.
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STAL\(_{AGE}\): STAL with the AGE strategy.
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STAL\(_{rev}\): A model similar to STAL\(_{\epsilon }\) except it applies the self-training strategy before the active learning selection.
Method | Cora | Citeseer | Pubmed | ogbn-arxiv |
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GCN | 77.7±2.2 | 63.3±3.1 | 75.0±2.8 | 61.6±0.6 |
ST | 77.9±2.5 | 63.5±5.2 | 74.9±3.1 | 61.7±1.2 |
AL\(_{\epsilon }\) | 77.8±3.6 | 64.0±2.3 | 74.8±2.9 | 61.9±1.5 |
AL\(_{QbC}\) | 78.1±1.2 | 64.2±1.6 | 74.9±2.4 | 62.1±0.8 |
AL\(_{AGE}\) | 79.3±1.5 | 65.5±2.4 | 78.1±1.1 | 61.9±0.3 |
STAL\(_{\epsilon }\) | 78.9±2.4 | 67.9±2.8 | 76.0±2.6 | 62.5±0.5 |
STAL\(_{QbC}\) | 78.9±1.3 | 68.1±1.6 | 76.2±1.8 | 62.9±0.02 |
STAL\(_{AGE}\) | 80.8±1.9 | 65.6±1 | 79.7±1.2 | 62.6±0.07 |
STAL\(_{rev}\) | 78.7±2.1 | 66.8±3.5 | 76.0±2.8 | 62.4±0.7 |
5.2.2 Quality and size of pseudo-labels
5.2.3 Number of active learning rounds k
GNN | Strategy | Cora | Citeseer | PubMed | ogbn-arxiv |
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GCN | Vanilla | 77.7±2.2 | 63.3±3.1 | 75.0±2.8 | 61.6±0.6 |
\(\hbox {STAL}_{\epsilon }\) | 78.9±2.4 | \(\underline{{\textbf {67.9}}\pm {\textbf {2.8}}}\) | 76.0±2.6 | 62.5±0.5 | |
\(\hbox {STAL}_{AGE}\) | \(\underline{80.8\pm 1.9}\) | 65.6±1 | \(\underline{{\textbf {79.7}}\pm {\textbf {1.2}}}\) | \(\underline{62.6\pm 0.07}\) | |
SAGE | Vanilla | 72.3±1.8 | 59.3±1.6 | 71.3±2.2 | 59.0±0.4 |
STAL\(_{\epsilon }\) | \(\underline{{\textbf {81.8}}\pm {\textbf {0.8}}}\) | 66.5±2.2 | 74.3±1.6 | 61.6±0.7 | |
STAL\(_{AGE}\) | 78.2±2.2 | \(\underline{67.0\pm 1.9}\) | \(\underline{74.5\pm 2.1}\) | \(\underline{61.8\pm 0.08}\) | |
GAT | Vanilla | 77.4±1.6 | 60.1±2.6 | 76.0±2.7 | 63.1±0.9 |
STAL\(_{\epsilon }\) | \(\underline{81.2\pm 2.5}\) | \(\underline{67.46\pm 1.3}\) | 78.4±2.5 | 63.3±0.3 | |
STAL\(_{AGE}\) | 80.2±1.3 | 65.4±1.1 | \(\underline{78.8\pm 0.6}\) | \(\underline{{\textbf {63.7}}\pm {\textbf {0.04}}}\) |