Joint Detection and Classification in Unsupervised Graph Learning

LI Sicong; WANG Fei; WEI Ziling; CHEN Shuhui

doi:10.12263/DZXB.20250761

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Joint Detection and Classification in Unsupervised Graph Learning

PAPERS | 更新时间：2026-06-04

- Joint Detection and Classification in Unsupervised Graph Learning
- ACTA ELECTRONICA SINICA Vol. 54, Issue 1, Pages: 153-166(2026)
- 作者机构：
  
  国防科技大学计算机学院，湖南长沙 410073
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20250761
  CLC： TP181;
- Received：04 September 2025，
  
  Accepted：29 December 2025，
  
  Published：25 January 2026
- 稿件说明：
移动端阅览
李思聪, 王飞, 魏子令, 等. 一石二鸟：图数据无监督学习中的检测与分类协同[J]. 电子学报, 2026, 54(01): 153-166.

LI Sicong, WANG Fei, WEI Ziling, et al. Joint Detection and Classification in Unsupervised Graph Learning[J]. Acta Electronica Sinica, 2026, 54(01): 153-166.
李思聪, 王飞, 魏子令, 等. 一石二鸟：图数据无监督学习中的检测与分类协同[J]. 电子学报, 2026, 54(01): 153-166. DOI：10.12263/DZXB.20250761

LI Sicong, WANG Fei, WEI Ziling, et al. Joint Detection and Classification in Unsupervised Graph Learning[J]. Acta Electronica Sinica, 2026, 54(01): 153-166. DOI：10.12263/DZXB.20250761

摘要

现实世界中的图机器学习系统通常运行于开放环境，测试阶段不可避免地接触到与训练分布不一致的样本，这违背了传统监督学习中训练与测试同分布的假设。模型不仅需要在分布内（In-Distribution，ID）样本上保持稳定的分类性能，还需具备识别并拒绝分布外（Out-Of-Distribution，OOD）数据的能力，以避免过度自信的错误预测。由于图数据中节点属性与拓扑结构高度耦合，分布偏移往往以隐式形式发生，使得图OOD检测较欧氏数据更加复杂。现有图OOD检测方法通常依赖强监督假设，如引入预标注的异常样本，或假设辅助OOD数据与ID数据在特征空间中显著可分。然而在实际应用中，OOD数据多以无标注、与ID数据天然混杂的形式出现，例如社交网络中的跨平台用户或推荐系统中的冷启动节点。这类野生数据难以通过先验规则进行显式区分，限制了现有方法在开放环境下的适用性。针对这一问题，本文提出一种全开放训练范式，在无需任何OOD标注或分布先验的条件下，利用无标注ID/OOD混合数据联合优化图节点分类与OOD检测任务。该方法通过构建带约束的优化目标，在严格约束ID分类误差与误检率的同时，引导模型提升对潜在OOD样本的识别能力，从而刻画真实开放环境中ID与OOD分布的隐式耦合关系。在方法层面，引入基于能量函数的检测机制，将图神经网络输出映射为能量值以度量样本与训练分布的一致性。能量约束引导模型在表示空间中形成可分离的分布结构，使ID样本集中于低能量区域，而潜在OOD样本对应较高能量，从而实现有效区分。该机制避免了基于Softmax置信度方法在分布外场景下的过度自信问题，并使检测目标能够直接作用于图表示学习过程。为求解上述带约束优化问题，本文采用增广拉格朗日方法，在训练过程中动态平衡约束满足与目标优化，增强模型在混合分布下的稳定性。实验结果显示，该方法在多个真实世界图数据集上均取得显著性能提升。在Twitch数据集上，AUROC和AUPR分别达到95.97%和92.84%，较当前最优基线GNNsafe++提升超过21个百分点，同时将误报率控制在12.30%，验证了其在无强监督条件下的有效性与鲁棒性。

Abstract

Real-world graph machine learning systems typically operate in open environments

where test-time data inevitably deviate from the training distribution

violating the common assumption of identical training and testing distributions in supervised learning. In this setting

models are required not only to maintain stable classification performance on in-distribution (ID) samples

but also to accurately identify and reject out-of-distribution (OOD) data to avoid overconfident erroneous predictions. Due to the strong coupling between node attributes and graph topology

distribution shifts in graph data often occur implicitly

making graph OOD detection more challenging than its Euclidean counterpart. Existing graph OOD detection methods commonly rely on strong supervision assumptions

such as the availability of pre-labeled anomalous samples or the assumption that auxiliary OOD data are clearly separable from ID data in the feature space. However

in practical applications

OOD samples typically appear in an unlabeled and naturally mixed manner with ID data

as observed in cross-platform users in social networks or cold-start nodes in recommendation systems. Such wild data are difficult to distinguish using prior rules

which limits the applicability of existing approaches in open environments. To address this issue

we propose a fully open training paradigm that jointly optimizes graph node classification and OOD detection using unlabeled ID/OOD mixed data

without requiring any OOD annotations or distributional priors. The proposed method formulates a constrained optimization objective that strictly controls ID classification error and false positive rates

while encouraging the model to improve its capability to identify potential OOD samples

thereby capturing the implicit coupling between ID and OOD distributions in real-world open settings. At the methodological level

we introduce an energy-based detection mechanism that maps the outputs of graph neural networks to energy values

which quantify the consistency of samples with the training distribution. The imposed energy constraints guide the model to learn separable representations

where ID samples concentrate in low-energy regions while potential OOD samples are pushed toward higher-energy regions. This design alleviates the overconfidence issue of Softmax-based confidence methods under distribution shifts and allows the detection objective to directly influence graph representation learning. To effectively solve the resulting constrained optimization problem

we adopt an augmented Lagrangian approach that dynamically balances constraint satisfaction and objective optimization during training

enhancing model stability under mixed distributions. Experimental results on multiple real-world graph datasets demonstrate significant performance improvements. On the Twitch dataset

the proposed method achieves an AUROC of 95.97% and an AUPR of 92.84%

outperforming the current state-of-the-art baseline GNNsafe++ by over 21 percentage points

while maintaining a false positive rate of 12.30%. These results confirm the effectiveness and robustness of the proposed framework under fully unsupervised and open-world conditions.

关键词

Keywords

references

Guo Xiaoyu , Liu Yan , Gong Daofu , et al . Dual graph convolutional networks for social network alignment [J ] . IEEE Transactions on Big Data , 2025 , 11 ( 2 ): 684 - 695 . DOI: 10.1109/tbdata.2024.3423699 http://dx.doi.org/10.1109/tbdata.2024.3423699

Zhang Xiaomeng , Liang Li , Liu Lin , et al . Graph neural networks and their current applications in bioinformatics [J ] . Frontiers in Genetics , 2021 , 12 : 690049 . DOI: 10.3389/fgene.2021.690049 http://dx.doi.org/10.3389/fgene.2021.690049

Wu Shiwen , Sun Fei , Zhang Wentao , et al . Graph neural networks in recommender systems: A survey [J ] . ACM Computing Surveys , 2023 , 55 ( 5 ): 1 - 37 . DOI: 10.1145/3535101 http://dx.doi.org/10.1145/3535101

Nguyen A , Yosinski J , Clune J . Deep neural networks are easily fooled: High confidence predictions for unrecognizable images [C ] // 2015 IEEE Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE , 2015 : 427 - 436 . DOI: 10.1109/cvpr.2015.7298640 http://dx.doi.org/10.1109/cvpr.2015.7298640

Bevandić P , Šegvić S , Krešo I , et al . Discriminative out-of-distribution detection for semantic segmentation [C ] // Proceedings of the 7th International Conference on Learning Representations . Munich : OpenReview.net , 2019 : 18 - 36 . DOI: 10.1007/978-3-030-33676-9_3 http://dx.doi.org/10.1007/978-3-030-33676-9_3

Kukar M . Transductive reliability estimation for medical diagnosis [J ] . Artificial Intelligence in Medicine , 2003 , 29 ( 1/2 ): 81 - 106 . DOI: 10.1016/s0933-3657(03)00043-5 http://dx.doi.org/10.1016/s0933-3657(03)00043-5

Dai Dengxin , Van Gool L . Dark model adaptation: Semantic image segmentation from daytime to nighttime [C ] // 2018 21st International Conference on Intelligent Transportation Systems . Piscataway : IEEE , 2018 : 3819 - 3824 . DOI: 10.1109/itsc.2018.8569387 http://dx.doi.org/10.1109/itsc.2018.8569387

Nalisnick E , Matsukawa A , Teh Y W , et al . Do deep generative models know what they don’t know [C/OL ] // Proceedings of the 7th International Conference on Learning Representations . OpenReview . net , 2019 : https://openreview.net/pdf?id=H1xwNhCcYm https://openreview.net/pdf?id=H1xwNhCcYm .

席亮 , 刘涵 , 樊好义 , 等 . 基于深度对抗学习潜在表示分布的异常检测模型 [J ] . 电子学报 , 2021 , 49 ( 7 ): 1257 - 1265 . DOI: 10.12263/DZXB.20200970 http://dx.doi.org/10.12263/DZXB.20200970

Xi Liang , Liu Han , Fan Haoyi , et al . Deep adversarial learning latent representation distribution model for anomaly detection [J ] . Acta Electronica Sinica , 2021 , 49 ( 7 ): 1257 - 1265 . (in Chinese) . DOI: 10.12263/DZXB.20200970 http://dx.doi.org/10.12263/DZXB.20200970

Fang Zhen , Lu Jie , Zhang Guangquan . Out-of-distribution detection with non-semantic exploration [J ] . Information Sciences , 2025 , 705 : 121989 . DOI: 10.1016/j.ins.2025.121989 http://dx.doi.org/10.1016/j.ins.2025.121989

Hendrycks D , Gimpel K . A baseline for detecting misclassified and out-of-distribution examples in neural networks [C/OL ] // Proceedings of the 5th International Conference on Learning Representations . OpenReview . net , 2017 : https://openreview.net/references/pdf?id=Hkg4TI9xl https://openreview.net/references/pdf?id=Hkg4TI9xl .

DeVries T , Taylor G W . Learning confidence for out-of-distribution detection in neural networks [PP/OL ] . V1. arXiv ( 2018-02-13 )[ 2025-09-01 ] . https://doi.org/10.48550/arXiv.1802.04865 https://doi.org/10.48550/arXiv.1802.04865 .

Hein M , Andriushchenko M , Bitterwolf J . Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem [C ] // 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE , 2019 : 41 - 50 . DOI: 10.1109/cvpr.2019.00013 http://dx.doi.org/10.1109/cvpr.2019.00013

Hsu Y C , Shen Yilin , Jin Hongxia , et al . Generalized ODIN: Detecting out-of-distribution image without learning from out-of-distribution data [C ] // 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE , 2020 : 10948 - 10957 . DOI: 10.1109/cvpr42600.2020.01096 http://dx.doi.org/10.1109/cvpr42600.2020.01096

Sun Yiyou , Guo Chuan , Li Yixuan . ReAct: Out-of-distribution detection with rectified activations [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2021 : 144 - 157 .

Bitterwolf J , Meinke A , Augustin M , et al . Breaking down out-of-distribution detection: Many methods based on OOD training data estimate a combination of the same core quantities [C ] // Proceedings of the 39th International Conference on Machine Learning . PMLR , 2022 : 2041 - 2074 .

李思聪 , 王坚 , 宋亚飞 , 等 . TriCh-LKRepNet: 融合三通道映射与结构重参数化的大核卷积恶意代码分类网络 [J ] . 电子学报 , 2024 , 52 ( 7 ): 2331 - 2340 .

Li Sicong , Wang Jian , Song Yafei , et al . TriCh-LKRepNet: A large kernel convolutional malicious code classification network for structure reparameterisation and triple-channel mapping [J ] . Acta Electronica Sinica , 2024 , 52 ( 7 ): 2331 - 2340 . (in Chinese)

Liu Weitang , Wang Xiaoyun , Owens J D , et al . Energy-based out-of-distribution detection [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : ACM , 2020 : 21464 - 21475 .

Ranzato M , Boureau Y L , Chopra S , et al . A unified energy-based framework for unsupervised learning [C ] // Proceedings of the 11th International Conference on Artificial Intelligence and Statistics . San Juan : PMLR , 2007 : 371 - 392 .

Liang Shiyu , Li Yixuan , Srikant R . Enhancing the reliability of out-of-distribution image detection in neural networks [C ] // Proceedings of the 6th International Conference on Learning Representations . OpenReview . net , 2018 .

Cai Tingyi , Jiang Yunliang , Liu Yixin , et al . Out-of-distribution detection on graphs: A survey [PP/OL ] . V1. arXiv ( 2025-02-12 )[ 2026-03-30 ] . https://doi.org/10.48550/arXiv.2502.08105 https://doi.org/10.48550/arXiv.2502.08105 .

Li Haoyang , Wang Xin , Zhang Ziwei , et al . Out-of-distribution generalization on graphs: A survey [J ] . IEEE Transactions on Pattern Analysis and Machine Intelligence , 2025 , 47 ( 11 ): 10490 - 10512 . DOI: 10.1109/tpami.2025.3593897 http://dx.doi.org/10.1109/tpami.2025.3593897

Li Haoyang , Wang Xin , Zhang Ziwei , et al . GOOD: A graph out-of-distribution benchmark [C ] // Proceedings of the 36th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2022 : 068431 - 0150 . DOI: 10.52202/068431-0150 http://dx.doi.org/10.52202/068431-0150

Huang Tiancheng , Wang Donglin , Fang Yuan , et al . End-to-end open-set semi-supervised node classification with out-of-distribution detection [C ] // Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence . California : International Joint Conferences on Artificial Intelligence Organization , 2022 : 2087 - 2093 . DOI: 10.24963/ijcai.2022/290 http://dx.doi.org/10.24963/ijcai.2022/290

Bao Tianyi , Wu Qitian , Jiang Zetian , et al . Graph out-of-distribution detection goes neighborhood shaping [C ] // Proceedings of the 41st International Conference on Machine Learning . New York : ACM , 2024 : 2923 - 2943 .

Wang Yili , Liu Yixin , Shen Xu . Unifying unsupervised graph-level anomaly detection and out-of-distribution detection: A benchmark [C/OL ] // Proceedings of the 13th International Conference on Learning Representations . OpenReview . net , 2025 : https://openreview.net/forum?id=g90RNzs8wX https://openreview.net/forum?id=g90RNzs8wX .

Zhao Xujiang , Chen Feng , Hu Shu , et al . Uncertainty aware semi-supervised learning on graph data [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2020 : 1076 .

Stadler M , Charpentier B , Geisler S , et al . Graph posterior network: Bayesian predictive uncertainty for node classification [C ] // Proceedings of the 35th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2021 : 1380 .

Guo Jingwei , Huang Kaizhu , Yi Xinping , et al . Learning disentangled graph convolutional networks locally and globally [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2024 , 35 ( 3 ): 3640 - 3651 . DOI: 10.1109/tnnls.2022.3195336 http://dx.doi.org/10.1109/tnnls.2022.3195336

Yang Yiding , Feng Zunlei , Song Mingli , et al . Factorizable graph convolutional networks [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : ACM , 2020 : 20286 - 20296 .

Bevilacqua B , Zhou Yangze , Ribeiro B . Size-invariant graph representations for graph classification extrapolations [C ] // Proceedings of the 38th International Conference on Machine Learning . Cambridge : PMLR , 2021 : 837 - 851 .

Fan Shaohua , Wang Xiao , Shi Chuan , et al . Generalizing graph neural networks on out-of-distribution graphs [J ] . IEEE Transactions on Pattern Analysis and Machine Intelligence , 2024 , 46 ( 1 ): 322 - 337 . DOI: 10.1109/TPAMI.2023.3321097 http://dx.doi.org/10.1109/TPAMI.2023.3321097

Ganguly D , Gupta D . Detecting out-of-distribution data with semi-supervised graph “feature” networks [C/OL ] // Proceedings of the 11th International Conference on Learning Representations . OpenReview . net , 2023 : https://openreview.net/forum?id=0OlEBibFa_g https://openreview.net/forum?id=0OlEBibFa_g .

Ackley D , Hinton G , Sejnowski T . A learning algorithm for Boltzmann machines [J ] . Cognitive Science , 1985 , 9 ( 1 ): 147 - 169 . DOI: 10.1016/s0364-0213(85)80012-4 http://dx.doi.org/10.1016/s0364-0213(85)80012-4

Salakhutdinov R , Larochelle H . Efficient learning of deep Boltzmann machines [C ] // Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics . Cambridge : JMLR , 2010 : 693 - 700 .

Du Yilun , Li Shuang , Sharma Y , et al . Unsupervised learning of compositional energy concepts [C ] // Proceedings of the 35th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2021 : 15608 - 15620 .

Cong Tianji , Prakash A . Sneakoscope: Revisiting unsupervised out-of-distribution detection [C/OL ] // Proceedings of the 10th International Conference on Learning Representations . OpenReview . net , 2022 .

Ranzato M , Poultney C , Chopra S , et al . Efficient learning of sparse representations with an energy-based model [M ] //Schölkopf B, Platt J, Hofmann T. Advances in neural information processing systems 19 . Cambridge : The MIT Press , 2007 : 1137 - 1144 . DOI: 10.7551/mitpress/7503.003.0147 http://dx.doi.org/10.7551/mitpress/7503.003.0147

Xu Pingmei , Ehinger K A , Zhang Yinda , et al . TurkerGaze: Crowdsourcing saliency with webcam based eye tracking [PP/OL ] . V2. arXiv ( 2015-05-20 )[ 2025-09-01 ] . https://doi.org/10.48550/arXiv.1504.06755 https://doi.org/10.48550/arXiv.1504.06755 .

Grathwohl W , Wang K C , Jacobsen J H , et al . Learning the Stein discrepancy for training and evaluating energy-based models without sampling [C ] // Proceedings of the 37th International Conference on Machine Learning . New York : ACM , 2020 : 3732 - 3747 .

Liu Yixin , Li Shiyuan , Zheng Yu , et al . ARC: A generalist graph anomaly detector with in-context learning [C ] // Proceedings of the 38th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2024 : 1606 . DOI: 10.52202/079017-1606 http://dx.doi.org/10.52202/079017-1606

Pan Junjun , Liu Yixin , Zheng Xin , et al . A label-free heterophily-guided approach for unsupervised graph fraud detection [J ] . Proceedings of the AAAI Conference on Artificial Intelligence , 2025 , 39 ( 12 ): 12443 - 12451 . DOI: 10.1609/aaai.v39i12.33356 http://dx.doi.org/10.1609/aaai.v39i12.33356

Zheng Xin , Liu Yixin , Bao Zhifeng , et al . Towards data-centric graph machine learning: Review and outlook [PP/OL ] . V1. arXiv ( 2023-09-20 )[ 2026-03-30 ] . https://doi.org/10.48550/arXiv.2309.10979 https://doi.org/10.48550/arXiv.2309.10979 .

Feng Wenzheng , Zhang Jie , Dong Yuxiao , et al . Graph random neural networks for semi-supervised learning on graphs [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2020 : 1853 .

Kong Kezhi , Li Guohao , Ding Mucong , et al . Robust optimization as data augmentation for large-scale graphs [C ] // 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE , 2022 : 60 - 69 . DOI: 10.1109/cvpr52688.2022.00016 http://dx.doi.org/10.1109/cvpr52688.2022.00016

Zhao Tong , Liu Y , Neves L , et al . Data augmentation for graph neural networks [J ] . Proceedings of the AAAI Conference on Artificial Intelligence , 2021 , 35 ( 12 ): 11015 - 11023 . DOI: 10.1609/aaai.v35i12.17315 http://dx.doi.org/10.1609/aaai.v35i12.17315

Hestenes M R . Multiplier and gradient methods [J ] . Journal of Optimization Theory and Applications , 1969 , 4 ( 5 ): 303 - 320 . DOI: 10.1007/bf00927673 http://dx.doi.org/10.1007/bf00927673

Sen P , Namata G , Bilgic M , et al . Collective classification in network data [J ] . AI Magazine , 2008 , 29 ( 3 ): 93 - 106 . DOI: 10.1609/aimag.v29i3.2157 http://dx.doi.org/10.1609/aimag.v29i3.2157

Hu Weihua , Fey M , Zitnik M , et al . Open graph benchmark: Datasets for machine learning on graphs [C ] // Proceedings of the 34th International Conference on Neural Information Processing Systems . New York : Curran Associates Inc. , 2020 : 1855 . DOI: 10.48550/arXiv.2005.00687 http://dx.doi.org/10.48550/arXiv.2005.00687

McAuley J , Targett C , Shi Qinfeng , et al . Image-based recommendations on styles and substitutes [C ] // Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval . New York : ACM , 2015 : 43 - 52 . DOI: 10.1145/2766462.2767755 http://dx.doi.org/10.1145/2766462.2767755

Sinha A , Shen Zhihong , Song Yang , et al . An overview of microsoft academic service (MAS) and applications [C ] // Proceedings of the 24th International Conference on World Wide Web . New York : ACM , 2015 : 243 - 246 . DOI: 10.1145/2740908.2742839 http://dx.doi.org/10.1145/2740908.2742839

Rozemberczki B , Sarkar R . Twitch gamers: A dataset for evaluating proximity preserving and structural role-based node embeddings [PP/OL ] . V2.arXiv ( 2021-02-16 )[ 2025-09-01 ] . https://doi.org/10.48550/arXiv.2101.03091 https://doi.org/10.48550/arXiv.2101.03091 .

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