基于分数阶图神经扩散的跨频域对齐对比学习方法

王友清; 徐世龙; 赵天祥; 王宇晨; 辛梦媛; 张琦; 苏烨; 郭继鹏

doi:10.16383/j.aas.c250604

基于分数阶图神经扩散的跨频域对齐对比学习方法

doi: 10.16383/j.aas.c250604 cstr: 32138.14.j.aas.c250604

王友清^1,,
徐世龙^1,,
赵天祥^1,,
王宇晨^1,,
辛梦媛^1,,
张琦^2,,
苏烨^3,,
郭继鹏^1,

1.
北京化工大学信息科学与技术学院北京 100029
2.
山东农业大学信息科学与工程学院泰安 271018
3.
中国科学院深圳先进技术研究院深圳 518055

基金项目: 国家重点研发项目(2024YFB3311405), 国家自然科学基金(62225303, 62403043)资助

详细信息

作者简介:
王友清：北京化工大学信息科学与技术学院教授. 主要研究方向为工业大数据分析. E-mail: wang_youqing@buct.edu.cn

徐世龙：北京化工大学信息科学与技术学院硕士研究生. 主要研究方向为图神经网络和图表示学习. E-mail: xushilong@buct.edu.cn

赵天祥：北京化工大学信息科学与技术学院硕士研究生. 主要研究方向为机器学习. E-mail: tianxiangzhao@buct.edu.cn

王宇晨：北京化工大学信息科学与技术学院硕士研究生. 主要研究方向为图神经网络和图异常检测. E-mail: 2025200789@buct.edu.cn

辛梦媛：北京化工大学信息科学与技术学院博士研究生. 主要研究方向为对抗样本学习. E-mail: 2025400300@buct.edu.cn

张琦：山东农业大学信息科学与工程学院副教授. 主要研究方向为图机器学习, 知识图谱和大语言模型. E-mail: QiZhang2025@sdau.edu.cn

苏烨：中国科学院深圳先进技术研究院博士研究生. 主要研究方向为机器学习与模式识别. E-mail: ye.su@siat.ac.cn

郭继鹏：北京化工大学信息科学与技术学院副教授. 主要研究方向为机器学习、模式识别和工业过程数据分析. 本文通信作者. E-mail: guojipeng@buct.edu.cn

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出版历程
- 收稿日期: 2025-11-05
- 录用日期: 2026-01-20
- 网络出版日期: 2026-03-30
- 刊出日期: 2026-06-20

Fractional-order Graph Neural Diffusion for Cross-frequency Alignment Contrastive Learning

1.
College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029
2.
School of Information Science and Engineering, Shandong Agricultural University, Taian 271018
3.
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055

Funds: Supported by National Key Research and Development Program of China (2024YFB3311405) and National Natural Science Foundation of China (62225303, 62403043)

More Information

Author Bio:
WANG You-Qing　Professor at the College of Information Science and Technology, Beijing University of Chemical Technology. His main research interest is industrial big data analysis

XU Shi-Long　Master student at the College of Information Science and Technology, Beijing University of Chemical Technology. His research interests include graph neural network and graph representation learning

ZHAO Tian-Xiang　Master student at the College of Information Science and Technology, Beijing University of Chemical Technology. His main research interest is machine learning

WANG Yu-Chen　Master student at the College of Information Science and Technology, Beijing University of Chemical Technology. His research interests include graph neural networks and graph anomaly detection

XIN Meng-Yuan　Ph.D. candidate at the College of Information Science and Technology, Beijing University of Chemical Technology. Her main research interest is adversarial example learning

ZHANG Qi　Associate professor at the School of Information Science and Engineering, Shandong Agricultural University. His research interests include graph machine learning, knowledge graph and large language models

SU Ye　Ph.D. candidate at Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences. His research interests include machine learning and pattern recognition

GUO Ji-Peng　Associate professor at the College of Information Science and Technology, Beijing University of Chemical Technology. His research interests include machine learning, pattern recognition and industrial process data analysis. Corresponding author of this paper

摘要

摘要: 图对比学习(GCL)作为一种强大的自监督表示学习范式, 能够通过有效利用无标签数据来增强半监督学习中的表示判别性和泛化能力. 然而, 现有的GCL方法在学习判别性嵌入表示以及图数据增强过程中实现对比多样性与语义一致性之间的平衡方面存在困难, 这导致在构建增强视图时关键信息的丢失. 为解决这些挑战, 提出一种新颖的跨频域对齐对比学习(CfACL)框架, 利用分数阶图神经扩散(FGND)进行图节点表示学习. FGND利用切比雪夫多项式分数阶微分方程实现图信号中多阶邻域信息的远程扩散, 缓解过平滑问题并提高图嵌入表示的判别能力. 随后, 通过高频和低频滤波器分别构建两种不同的FGND形式, 形成自然的增强对比视图, 避免了随机增强引起的内在结构坍塌和语义漂移. CfACL方法将高频滤波分量转换到低频域, 并在镜像的虚拟谱空间中进行对比学习, 从而能够在全局一致的语义空间中吸收有益的高频细节, 为下游任务生成全面的表示. 在同配性和异配性基准图数据集上的大量节点分类实验结果验证了所提方法的有效性.
- 图对比学习 /
- 分数阶图扩散 /
- 高频滤波 /
- 低频滤波 /
- 跨频域对齐
Abstract: Graph contrastive learning (GCL), a powerful self-supervised representation learning paradigm, could enhance representation discriminability and generalization in semi-supervised learning by effectively leveraging unlabeled data. However, existing GCL methods struggle to learn discriminative embedding and achieve better balance between contrastive diversity and semantic invariance during graph data augmentation, inevitably leading to the critical information loss when constructing augmented views. To address these challenges, this paper proposes a novel cross-frequency alignment contrastive learning (CfACL) framework with fractional-order graph neural diffusion (FGND) for graph node representation learning. The FGND leverages Chebyshev polynomial fractional differential equations to achieve the long-range diffusion of multi-order neighboring information, alleviating over-smoothing and improving the discriminability of graph representation. Then, two distinct FGNDs are characterized by high-frequency and low-frequency filters to form natural augmented contrastive views, avoiding the intrinsic structure collapse and semantic shift caused by random augmentation. The CfACL transforms high-frequency filtered components into the low-frequency domain and achieves the contrastive learning in mirrored virtual spectral space, which is capable of absorbing beneficial high-frequency details in a globally consistent semantic space and results in comprehensive representation for downstream tasks. Extensive node classification experiments demonstrate the effectiveness of the proposed method across homophilic and heterophilic benchmark graph datasets.
- graph contrastive learning /
- fractional-order graph diffusion /
- high-frequency filtering /
- low-frequency filtering /
- cross-frequency alignment

HTML全文

图 1 消融实验结果

Fig. 1 The results of ablation experiment

下载: 全尺寸图片幻灯片

图 2 CfACL使用不同对比学习损失在数据集Cornell上的实验结果

Fig. 2 The experimental results of CfACL with various contrastive learning losses on the Cornell dataset

下载: 全尺寸图片幻灯片

图 3 CfACL关于不同时间$t $的实验结果

Fig. 3 The experimental results of CfACL with various time $t $

下载: 全尺寸图片幻灯片

图 4 CfACL在时间$ t\in \{4,\; 8,\; 16,\; 32,\; 64\} $下的分类性能

Fig. 4 The classification performance of CfACL when time $ t\in \{4,\; 8,\; 16,\; 32,\; 64\} $

下载: 全尺寸图片幻灯片

图 5 在Cora和Cornell数据集上的t-SNE可视化结果

Fig. 5 The t-SNE visualization results on the Cora and Cornell datasets

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图 6 在Cora和Chameleon数据集上的训练损失和分类准确率随训练迭代步数的变化

Fig. 6 The variation of training loss and classification accuracy with training iteration epochs on Cora and Chameleon datasets

下载: 全尺寸图片幻灯片

表 1 数据集统计信息

Table 1 The statistics of the datasets

数据集	节点数量	边数量	特征数量	类别数量	边同配性比
Cora	2708	5429	1433	7	0.81
Citeseer	3327	4732	3703	6	0.73
PubMed	19717	88651	500	3	0.80
Wisconsin	251	466	1703	5	0.17
Texas	183	309	1793	5	0.06
Cornell	183	295	1703	5	0.12
Chameleon	2277	36101	2325	5	0.23
Squirrel	5201	217073	2089	5	0.20
Actor	7600	33391	932	5	0.21

下载: 导出CSV

表 2 在同配性和异配性数据集上的节点分类实验结果(%)

Table 2 The node classification experiment results on homophilic and heterophilic datasets (%)

方法	Cora	Citeseer	PubMed	Wisconsin	Cornell	Texas	Chameleon	Squirrel	Actor
DGI	$ 82.30\pm0.60 $	$ 71.80\pm0.70 $	$ 76.80\pm0.60 $	$ 55.21\pm1.02 $	$ 45.33\pm6.11 $	$ 58.53\pm2.98 $	$ 60.27\pm0.70 $	$ 26.44\pm1.12 $	$ 28.30\pm0.76 $
GCA	$ 82.93\pm0.42 $	$ 72.19\pm0.31 $	$ 80.79\pm0.45 $	$ 59.55\pm0.81 $	$ 52.31\pm1.09 $	$ 52.92\pm0.46 $	$ 63.66\pm0.32 $	$ 48.09\pm0.21 $	$ 28.47\pm0.29 $
CCA-SSG	$ 84.00\pm0.40 $	$ 73.10\pm0.30 $	$ 81.00\pm0.40 $	$ 58.46\pm0.96 $	$ 52.17\pm1.04 $	$ 59.89\pm0.78 $	$ 62.41\pm0.22 $	$ 46.76\pm0.36 $	$ 27.82\pm0.60 $
BGRL	$ 82.70\pm0.60 $	$ 71.10\pm0.80 $	$ 79.60\pm0.50 $	$ 51.23\pm1.17 $	$ 50.33\pm2.29 $	$ 52.77\pm1.98 $	$ 64.86\pm0.63 $	$ 36.22\pm1.97 $	$ 28.80\pm0.54 $
SP-GCL	$ 83.16\pm0.13 $	$ 71.96\pm0.42 $	$ 79.16\pm0.84 $	$ 60.12\pm0.39 $	$ 52.29\pm1.21 $	$ 59.81\pm1.33 $	$ 65.28\pm0.53 $	$ 52.10\pm0.67 $	$ 28.94\pm0.69 $
GraphACL	$ \underline{84.20\pm0.31} $	$ \underline{73.63\pm0.22} $	$ \underline{82.02\pm0.15} $	$ 69.22\pm0.40 $	$ \underline{59.33\pm1.48} $	$ 71.08\pm0.34 $	$ \underline{69.12\pm0.24} $	$ \underline{54.05\pm0.13} $	$ 30.03\pm0.13 $
PolyGCL	$ 81.97\pm0.19 $	$ 71.97\pm0.29 $	$ 77.48\pm0.39 $	$ \underline{76.08\pm3.33} $	$ 43.78\pm3.51 $	$ \underline{72.16\pm3.51} $	$ 46.84\pm1.53 $	$ 34.25\pm0.66 $	$ \underline{34.37\pm0.69} $
CfACL	$ {\bf{85.17}}\pm{\bf{1.51}} $	$ {\bf{76.67}}\pm{\bf{1.38}} $	$ {\bf{86.37}}\pm{\bf{1.26}} $	$ {\bf{80.34}}\pm{\bf{0.47}} $	$ {\bf{71.70}}\pm{\bf{7.43}} $	$ {\bf{83.14}}\pm{\bf{5.34}} $	$ {\bf{72.29}}\pm{\bf{1.50}} $	$ {\bf{62.54}}\pm{\bf{1.14}} $	$ {\bf{36.76}}\pm{\bf{1.34}} $

下载: 导出CSV

表 3 CfACL与代表性对比方法PolyGCL和GraphACL在不同数据集上的训练成本对比(s)

Table 3 The comparison of training costs for CfACL versus the representative comparison methods PolyGCL and GraphACL across different datasets (s)

方法	Cora	PubMed	Chameleon	Cornell	Texas	Actor
PolyGCL	23.42	4392.96	19.62	32.29	24.03	54.71
GraphACL	23.08	340.35	212.19	28.10	27.64	3888.55
CfACL	19.58	108.86	19.58	22.79	29.96	32.99

下载: 导出CSV

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