Particle Competition and Cooperation for Robust Graph Convolutional Network Learning Under Label Noise

Fabricio Breve

cs.LGSep 18, 2026

Particle Competition and Cooperation for Robust Graph Convolutional Network Learning Under Label Noise

Authors: Fabricio Breve

Organizations: São Paulo State University - UNESP, Rio Claro - SP, Brazil

Abstract

Graph Convolutional Networks (GCNs) are highly sensitive to label noise, since corrupted supervision can propagate through the graph and degrade learned node representations. This work proposes PCC+GCN, a hybrid framework that uses Particle Competition and Cooperation (PCC) as a graph-based label-refinement stage before GCN training. PCC identifies suspicious labeled nodes through particle domination dynamics and determines whether their labels should be preserved, removed, or reassigned before GCN training. The framework also allows the graph used by PCC to be augmented with feature-based $k$ -nearest-neighbor edges, while the GCN itself is trained on the original graph structure and node features. The proposed method was evaluated on ten graph datasets from the NoisyGL benchmark under conventional Uniform, Pair, and Random label noise, as well as under instance-dependent label noise. A detailed hyperparameter analysis was also conducted on Cora, CiteSeer, and PubMed. Under conventional noise, PCC+GCN achieved the highest overall average accuracy and the best average rank among the evaluated methods, with an average gain of $1.67$ percentage points over the baseline GCN across the clean setting and all noisy scenarios. Under instance-dependent noise, PCC+GCN remained competitive with the best-performing robust methods while requiring substantially lower execution time, being the fastest robust method on eight of the ten datasets. The results indicate that PCC-based label refinement provides an effective and computationally efficient preprocessing strategy for improving GCN robustness under noisy supervision.

Figures & tables

Figure 1: The proposed framework.

Mode	Description
None	Original graph without additional $k$ -NN edges.
Same-Label	Add a $k$ -NN edge only when both endpoints are labeled and share the same class label.
Non-Conflicting	Add a $k$ -NN edge unless the endpoints have conflicting known labels. This includes pairs involving unlabeled nodes.
Full	Add all $k$ -NN edges regardless of label information.

Table 1: k-NN augmentation modes evaluated in the proposed framework.

Dataset	# Nodes	# Edges	Features	# Classes	Homophily	Avg. Degree	HP Analysis
Cora	2,708	5,278	1,433	7	0.81	3.90	✓
CiteSeer	3,327	4,552	3,703	6	0.74	2.74	✓
PubMed	19,717	44,324	500	3	0.80	4.50	✓
Amazon-Computers	13,752	491,722	767	10	0.78	35.8
Amazon-Photos	7,650	238,162	745	8	0.83	31.1
DBLP	17,716	105,734	1,639	4	0.83	5.97

Table 2: Characteristics of the datasets used in this work (adapted from Wang et al. (2024) ).

Figure 2: Heatmaps for the Cora dataset with different noise rates, greedy-walk probabilities, and distance exponents.

Figure 3: Heatmaps for the CiteSeer dataset with different noise rates, greedy-walk probabilities, and distance exponents.

Figure 4: Heatmaps for the PubMed dataset with different noise rates, greedy-walk probabilities, and distance exponents.

Dataset	$\boldsymbol{p_{\mathrm{grd}}}$	$\boldsymbol{d_{\mathrm{exp}}}$	$\boldsymbol{\tau_{\mathrm{rem}}}$	$\boldsymbol{\tau_{\mathrm{rel}}}$
Cora	0.1	3	0.1	0.1
CiteSeer	0.0	0	0.1	0.1
PubMed	0.4	2	0.1	0.1

Table 3: PCC hyperparameter configurations selected from the hyperparameter analysis.

Figure 5: Heatmaps for the Cora dataset with different noise rates, removal and relabeling thresholds.

Figure 6: Heatmaps for the CiteSeer dataset with different noise rates, removal and relabeling thresholds.

Figure 7: Heatmaps for the PubMed dataset with different noise rates, removal and relabeling thresholds.

Figure 8: Heatmaps for the Cora dataset with different noise rates, graph augmentation modes, and numbers of nearest-neighbor edges added.

Figure 9: Heatmaps for the CiteSeer dataset with different noise rates, graph augmentation modes, and numbers of nearest-neighbor edges added.

Figure 10: Heatmaps for the PubMed dataset with different noise rates, graph augmentation modes, and numbers of nearest-neighbor edges added.

Noise	Rate	Cora	CiteSeer	PubMed	Amazon-C	Amazon-P	DBLP	BlogCatalog	Flickr	Amz-Rat.	Roman-Emp.
Clean	Clean	$82.03{\scriptscriptstyle\pm}0.51$	$72.53{\scriptscriptstyle\pm}0.89$	$78.99{\scriptscriptstyle\pm}0.60$	$82.16{\scriptscriptstyle\pm}0.54$	$91.26{\scriptscriptstyle\pm}0.43$	$78.71{\scriptscriptstyle\pm}0.41$	$74.87{\scriptscriptstyle\pm}0.83$	$59.75{\scriptscriptstyle\pm}0.79$	$40.19{\scriptscriptstyle\pm}0.18$	$42.63{\scriptscriptstyle\pm}0.24$
Uniform	0.1	$80.83{\scriptscriptstyle\pm}1.27$	$70.39{\scriptscriptstyle\pm}1.37$	$74.18{\scriptscriptstyle\pm}3.23$	$81.38{\scriptscriptstyle\pm}0.94$	$89.02{\scriptscriptstyle\pm}1.67$	$76.25{\scriptscriptstyle\pm}1.32$	$73.23{\scriptscriptstyle\pm}1.31$	$56.60{\scriptscriptstyle\pm}0.94$	$39.60{\scriptscriptstyle\pm}0.53$	$40.75{\scriptscriptstyle\pm}0.74$
	0.2	$78.54{\scriptscriptstyle\pm}1.62$	$67.93{\scriptscriptstyle\pm}2.32$	$71.02{\scriptscriptstyle\pm}3.70$	$77.13{\scriptscriptstyle\pm}2.23$	$87.00{\scriptscriptstyle\pm}4.02$	$73.75{\scriptscriptstyle\pm}2.87$	$71.53{\scriptscriptstyle\pm}1.19$	$54.64{\scriptscriptstyle\pm}1.66$	$39.58{\scriptscriptstyle\pm}0.39$	$38.53{\scriptscriptstyle\pm}0.63$
	0.3	$72.08{\scriptscriptstyle\pm}3.31$	$63.93{\scriptscriptstyle\pm}3.19$	$63.12{\scriptscriptstyle\pm}7.20$	$74.20{\scriptscriptstyle\pm}3.17$	$85.97{\scriptscriptstyle\pm}2.96$	$68.82{\scriptscriptstyle\pm}2.70$	$70.36{\scriptscriptstyle\pm}1.85$	$51.71{\scriptscriptstyle\pm}2.00$	$39.37{\scriptscriptstyle\pm}0.47$	$36.66{\scriptscriptstyle\pm}0.48$
	0.4	$63.37{\scriptscriptstyle\pm}6.05$	$60.56{\scriptscriptstyle\pm}4.10$	$56.56{\scriptscriptstyle\pm}5.26$	$68.98{\scriptscriptstyle\pm}9.04$	$83.16{\scriptscriptstyle\pm}3.75$	$66.94{\scriptscriptstyle\pm}4.72$	$68.11{\scriptscriptstyle\pm}2.94$	$47.86{\scriptscriptstyle\pm}1.76$	$37.73{\scriptscriptstyle\pm}0.96$	$33.17{\scriptscriptstyle\pm}0.75$
	0.5	$57.96{\scriptscriptstyle\pm}9.38$	$51.98{\scriptscriptstyle\pm}4.84$	$48.00{\scriptscriptstyle\pm}10.53$	$62.47{\scriptscriptstyle\pm}7.78$	$76.89{\scriptscriptstyle\pm}5.15$	$62.75{\scriptscriptstyle\pm}5.77$	$61.16{\scriptscriptstyle\pm}4.86$	$43.51{\scriptscriptstyle\pm}2.70$	$36.65{\scriptscriptstyle\pm}1.30$	$33.63{\scriptscriptstyle\pm}0.66$

Table 4: Accuracy (%) of the proposed method in the NoisyGL Benchmark for all datasets, noise types and noise rates.

Noise

Rate

Cora

CiteSeer

PubMed

Amazon-C

Amazon-P

DBLP

BlogCatalog

Flickr

Amz-Rat.

Roman-Emp.

Average

Clean

+1.37

+3.52

+0.31

-2.57

-0.56

+1.68

-1.65

+3.00

+0.58

+5.66

+1.13

Uniform

0.1

+2.25

+4.91

-0.43

-1.68

-0.40

+1.01

-1.17

+1.16

+0.59

+5.78

+1.20

0.2

+2.62

+6.53

+0.76

-2.66

-1.02

+1.38

+0.23

+1.58

+1.05

+4.80

+1.53

0.3

+1.02

+8.88

-3.41

-3.06

+1.11

-0.84

+1.00

+1.94

+1.64

+4.08

+1.24

0.4

-4.51

+11.67

-1.30

-4.80

+3.83

+2.41

+3.38

+0.57

+0.83

+2.84

+1.49

0.5

+3.54

+8.47

-4.73

-5.47

+2.50

+5.70

+1.08

+0.56

-0.10

+6.07

+1.76

Table 5: Accuracy gain (percentage points) of the proposed method in the NoisyGL Benchmark for all datasets, noise types and noise rates, compared to the GCN baseline. Green and red cells indicate gains and losses greater than 0.5 percentage points in magnitude, respectively.

Method	Cora	CiteSeer	PubMed	Amazon-C	Amazon-P	DBLP	BlogCatalog	Flickr	Amz-Rat.	Roman-Emp.	Average
GCN	67.62	54.52	63.96	73.42	79.78	65.39	64.22	48.18	37.50	31.36	58.60
CGNN	66.37	51.15	56.36	43.74	47.19	58.51	24.15	11.77	34.09	18.83	41.21
CLNode	66.12	53.88	62.66	74.70	79.67	63.77	63.35	46.64	36.79	30.67	57.82
CP	68.22	54.99	64.36	72.94	78.74	66.79	63.25	42.75	37.62	30.47	58.01
CR-GNN	67.87	53.49	64.84	45.74	36.09	65.97	59.48	32.14	35.10	23.37	48.41
DGNN	57.72	47.97	61.64	49.56	55.05	62.85	42.55	17.17	34.34	21.24	45.01

Table 6: Global average accuracy by method (clean + all noisy types and rates). — indicates that the method does not report results for the corresponding dataset; averages involving RNCGLN are therefore computed over the available datasets.

Method	Cora	CiteSeer	PubMed	Amazon-C	Amazon-P	DBLP	BlogCatalog	Flickr	Amz-Rat.	Roman-Emp.	Average Rank
GCN	7	7	5	3	2	7	4	2	3	5	4.50
CGNN	9	10	11	11	10	12	12	12	11	11	10.90
CLNode	10	8	8	1	4	8	5	4	5	6	5.90
CP	5	6	3	4	5	4	6	5	2	7	4.70
CR-GNN	6	9	2	10	11	5	7	8	9	9	7.60
DGNN	12	12	9	9	9	10	11	11	10	10	10.30

Table 7: Ranking of methods by average accuracy in each dataset (clean + all noisy types and rates). — indicates that the method does not report results for the corresponding dataset; averages involving RNCGLN are therefore computed over the available datasets.

Figure 11: Average classification accuracy of all benchmark methods across all datasets for different label noise types and rates.

Figure 12: Average improvement in classification accuracy of all benchmark methods across all datasets relative to the baseline GCN, for different label noise types and rates.

Figure 13: Average classification accuracy of GCN, CP, NRGNN, PIGNN, and PCC+GCN across all datasets under instance-dependent label noise at different noise rates.

Figure 14: Average improvement in classification accuracy of CP, NRGNN, PIGNN, and PCC+GCN across all datasets relative to the baseline GCN under instance-dependent label noise at different noise rates.

Figure 15: Average classification accuracy of GCN, CP, NRGNN, PIGNN, and PCC+GCN on each dataset under instance-dependent label noise, considering noise rates from

10\%

50\%

Figure 16: Average CPU and GPU execution times of GCN, CP, NRGNN, PIGNN, and PCC+GCN on each dataset under instance-dependent label noise. The stacked bars represent the total execution time (CPU + GPU).

Learning with Noisy Labels

Learning with noisy labels studies how to train reliable models when annotations are incorrect, incomplete, subjective, or weakly supervised.

See all 148 papers

A Label Noise Robust Algorithm for Graph Data using Neighborhood Label Distribution
Oct 16, 2026Pintu Kumar, Nandyala HemachandraGraph Neural Networks Noisy-Label Learning
Indian Institute of Technology Bombay
Contrastive Adversarial Training for Robust Graph Neural Networks under Label Poisoning
Oct 17, 2026Manshika Charvi Bissessur, Melis Ilayda Bal, Michael MuehlebachGraph Neural Networks Robust Classification
University of Oxford · Max Planck Institute for Intelligent Systems, Tübingen, Germany · LIONS – École Polytechnique Fédérale de Lausanne +1
Towards Trustworthy Hypergraph Neural Networks under Label Noise
Aug 5, 2026Mengyao Zhou, Zhiheng Zhou, Xiao Han +1Graph Structure Learning Hypergraph Neural Networks
Academy of Mathematics and Systems Science, Chinese Academy of Sciences and also with the University of Chinese Academy of Sciences, Beijing 100190, China · School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China · School of Artificial Intelligence, Beihang University, Beijing 100191,China

Oct 16, 2026J/K move · Enter open · S save

A Label Noise Robust Algorithm for Graph Data using Neighborhood Label Distribution

Pintu Kumar, Nandyala Hemachandra

Indian Institute of Technology Bombay

Graph Neural Networks Noisy-Label Learning Node Classification

Open paper AskPDF arXiv

Graph Convolutional Networks (GCNs) have demonstrated exceptional performance on graph-structured data. However, their success heavily relies on the availability of clean labels, an assumption that often fails in real-world scenarios. The learnability of GCNs is intrinsically linked to the neighborhood structure of nodes, making it critical to understand how this structure changes in the presence of label noise. In this work, we investigate how the neighborhood label distribution of a node changes under label noise. We mathematically derive that label noise smooths this distribution, which inherently increases its entropy and severely decreases interclass distinguishability. To address this challenge, we propose Leave-one-out Entropy Node Screening (LENS), an end-to-end framework that identifies noisy nodes by measuring the reduction in neighborhood entropy when a specific node is removed. LENS further incorporates a relabeling mechanism to recover and preserve valuable feature information instead of entirely discarding the identified noisy nodes. Crucially, the end-to-end computational overhead of LENS is remarkably low. Extensive evaluations demonstrate that our algorithm achieves state-of-the-art node classification accuracy while executing an order of magnitude faster than existing noise-robust approaches.

Abstract

Learning with Noisy Labels

Explore similar work

A Label Noise Robust Algorithm for Graph Data using Neighborhood Label Distribution

Contrastive Adversarial Training for Robust Graph Neural Networks under Label Poisoning

Towards Trustworthy Hypergraph Neural Networks under Label Noise