Graph clustering is one of the fundamental tasks in graph data mining, with significant applications in social networks and recommendation systems. Traditional methods for clustering heterogeneous graphs typically involve obtaining node representations as a preliminary step, followed by the application of clustering algorithms to achieve the final clustering results. However, this two-step approach leads to a disconnection between the optimization of node representation and the clustering process, making it challenging to achieve optimal results. In this paper, we propose a graph clustering approach specifically designed for heterogeneous graphs that unifies the optimization of node representation and the clustering process for nodes in a heterogeneous graph. We assume that the relationships between different meta-paths in the heterogeneous graph are mutually independent. By maximizing the joint probability of meta-paths and nodes, we derive the optimization objective through variational methods. Finally, we employ backpropagation and reparameterization techniques to optimize this objective and thereby achieve the desired clustering results. Experiments conducted on multiple real heterogeneous datasets demonstrate that the proposed method is competitive with existing methods.
Citation: Chuang Ma, Helong Xia. A one-step graph clustering method on heterogeneous graphs via variational graph embedding[J]. Electronic Research Archive, 2024, 32(4): 2772-2788. doi: 10.3934/era.2024125
| [1] | Liandi Fang, Li Ma, Shihong Ding . Finite-time fuzzy output-feedback control for -norm stochastic nonlinear systems with output constraints. AIMS Mathematics, 2021, 6(3): 2244-2267. doi: 10.3934/math.2021136 |
| [2] | Yanghe Cao, Junsheng Zhao, Zongyao Sun . State feedback stabilization problem of stochastic high-order and low-order nonlinear systems with time-delay. AIMS Mathematics, 2023, 8(2): 3185-3203. doi: 10.3934/math.2023163 |
| [3] | Yihang Kong, Xinghui Zhang, Yaxin Huang, Ancai Zhang, Jianlong Qiu . Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers. AIMS Mathematics, 2024, 9(10): 28447-28471. doi: 10.3934/math.20241380 |
| [4] | Lu Zhi, Jinxia Wu . Adaptive constraint control for nonlinear multi-agent systems with undirected graphs. AIMS Mathematics, 2021, 6(11): 12051-12064. doi: 10.3934/math.2021698 |
| [5] | Yankui Song, Bingzao Ge, Yu Xia, Shouan Chen, Cheng Wang, Cong Zhou . Low-cost adaptive fuzzy neural prescribed performance control of strict-feedback systems considering full-state and input constraints. AIMS Mathematics, 2022, 7(5): 8263-8289. doi: 10.3934/math.2022461 |
| [6] | Jingjing Yang, Jianqiu Lu . Stabilization in distribution of hybrid stochastic differential delay equations with Lévy noise by discrete-time state feedback controls. AIMS Mathematics, 2025, 10(2): 3457-3483. doi: 10.3934/math.2025160 |
| [7] | Wei Zhao, Lei Liu, Yan-Jun Liu . Adaptive neural network control for nonlinear state constrained systems with unknown dead-zones input. AIMS Mathematics, 2020, 5(5): 4065-4084. doi: 10.3934/math.2020261 |
| [8] | Kunting Yu, Yongming Li . Adaptive fuzzy control for nonlinear systems with sampled data and time-varying input delay. AIMS Mathematics, 2020, 5(3): 2307-2325. doi: 10.3934/math.2020153 |
| [9] | Changgui Wu, Liang Zhao . Finite-time adaptive dynamic surface control for output feedback nonlinear systems with unmodeled dynamics and quantized input delays. AIMS Mathematics, 2024, 9(11): 31553-31580. doi: 10.3934/math.20241518 |
| [10] | Zhaohui Chen, Jie Tan, Yong He, Zhong Cao . Decentralized observer-based event-triggered control for an interconnected fractional-order system with stochastic Cyber-attacks. AIMS Mathematics, 2024, 9(1): 1861-1876. doi: 10.3934/math.2024091 |
Graph clustering is one of the fundamental tasks in graph data mining, with significant applications in social networks and recommendation systems. Traditional methods for clustering heterogeneous graphs typically involve obtaining node representations as a preliminary step, followed by the application of clustering algorithms to achieve the final clustering results. However, this two-step approach leads to a disconnection between the optimization of node representation and the clustering process, making it challenging to achieve optimal results. In this paper, we propose a graph clustering approach specifically designed for heterogeneous graphs that unifies the optimization of node representation and the clustering process for nodes in a heterogeneous graph. We assume that the relationships between different meta-paths in the heterogeneous graph are mutually independent. By maximizing the joint probability of meta-paths and nodes, we derive the optimization objective through variational methods. Finally, we employ backpropagation and reparameterization techniques to optimize this objective and thereby achieve the desired clustering results. Experiments conducted on multiple real heterogeneous datasets demonstrate that the proposed method is competitive with existing methods.
AIMS Energy is an Open Access international journal devoted to publishing peer-reviewed, high quality, original papers in the field of Energy science and technology, to promote the worldwide better understanding of full spectra of energy issues. Together with the Editorial Office of AIMS Energy, I wish to testify my sincere gratitude to all authors, members of the editorial board, and peer reviewers for their contribution to AIMS Energy in 2022.
In 2022, we had received 247 manuscripts, of which 58 have been accepted and published. These published papers include 40 research articles, 12 review articles, 4 editorial, and 2 opinion papers. The authors of the manuscripts are from more than 35 countries worldwide. The sources of the submissions showed a significant increase in international collaborations on the research of Energy technologies.
One of the important strategies of attracting high quality and high impact papers to our journal has been the calls for special issues. In 2022, 10 special issues were planned and called, and four of which have already published five high quality articles so far. Currently, there are 10 special issues open, and we expect to collect excellent articles for publication. AIMS Energy has 102 enthusiastic members on the editorial board, and 16 of them just joined in 2022. We will continue to renew and accept dedicated researchers to join the Editorial Board in 2023. Our members are active researchers, and we are confident that, with their dedicated effort, the journal will offer our readers more impactful publications.
With the high demand on innovative research for renewable energy and efficient utilization of energy, we expect to receive and collect more excellent articles being submitted to AIMS Energy in 2023. We would also like our members of the editorial board to encourage more of the peer researchers to publish papers and support AIMS Energy. The journal will dedicate to publishing high quality papers by both regular issues and special issues organized by the members of the editorial board. We believe that all these efforts will increase the impact and citations of the papers published by AIMS Energy.
Wish the best 2023 to our dedicated editorial board members, authors, peer reviewers, and staff members of the Editorial Office of AIMS Energy.
Prof. Peiwen (Perry) Li, Editor in Chief
AIMS Energy
Dept. of Aerospace and Mechanical Engineering,
University of Arizona, USA
The three-year manuscript statistics are shown below. In 2022, AIMS Energy published 6 issues, a total of 58 articles were published online, and the categories of published articles are as follows:
| Type | Number |
| Research Article | 40 |
| Review | 12 |
| Editorial | 4 |
| Opinion Paper | 2 |
|
Peer Review Rejection rate: 56%
Publication time (from submission to online): 90 days
An important part of our strategy of attracting high quality papers has been the call and preparation of special issues. In 2022, ten special issues were called by the editoral board members. Listed below are some examples of issues that have more than 5 papers. We encourage Editorial Board members to propose more potential topics, and to act as editors of special issues.
| Title | Link | Number of published |
| Analyzing energy storage systems for the applications of renewable energy sources | https://www.aimspress.com/aimse/article/6042/special-articles | 6 |
| Current Status and Future Prospects of Biomass Energy | https://www.aimspress.com/aimse/article/5988/special-articles | 5 |
| Hybrid renewable energy system design | https://www.aimspress.com/aimse/article/6313/special-articles | 5 |
AIMS Energy has Editorial Board members representing researchers from 23 countries, which are shown below.
We are constantly assembling the editorial board to be representative to a variety of disciplines across the field of Energy. AIMS Energy has 102 members now, and 16 of them joined in 2022. We will continue to invite dedicated experts and researchers, in order to renew the Editorial Board in 2023.
|
In the last few years, our journal has developed much faster than before; we received more than 200 manuscript submissions and published 58 papers in 2022. We have added 16 new Editorial Board members, and called for 10 special issues in 2022.
The growth of our journal will require us to invite dedicated and prestigious researchers and experts to our Editorial Board. Keeping this in mind, our first action in 2023 is to renew and rotate members of the Editorial Board. The foremost task is to invite more high-quality articles (Research and Review); especially the review articles to provide readers broad views on the technologies that interest us. We would like to increase the diversity of high-quality articles from all around the world. To set a goal, we would like to publish 60 high-quality articles in 2023. We hope Editorial Board members could help us invite some reputational scholars in your network and field to contribute articles to our journal.
Lastly, we would like to invite our board members to try to increase the influence and impact of AIMS Energy by soliciting and advertising high quality articles and special issues.
We really appreciate the time and effort of all our Editorial Board Members and Guest Editors, as well as our reviewers devoted to our journal in the difficult circumstances we have had in the last three years. All your excellent professional effort and expertise has provided us with very useful and professional suggestions in 2022. Last, but not least, thanks are given to the hard work of the in-house editorial team.
| [1] | N. Park, R. Rossi, E. Koh, I. A. Burhanuddin, S. Kim, F. Du, et al., CGC: Contrastive graph clustering for community detection and tracking, in Proceedings of the ACM Web Conference 2022, (2022), 1115–1126. https://doi.org/10.1145/3485447.3512160 |
| [2] |
L. Guo, Q. Dai, Graph clustering via variational graph embedding, Pattern Recognit., 122 (2022), 108334. https://doi.org/10.1016/j.patcog.2021.108334 doi: 10.1016/j.patcog.2021.108334
|
| [3] | R. A. Khan, M. Kleinsteuber, Cluster-aware heterogeneous information network embedding, in Proceedings of the Fifteenth ACM International Conference on Web Search and Data Mining, (2022), 476–486. https://doi.org/10.1145/3488560.3498385 |
| [4] |
C. Song, Y. Teng, Y. Zhu, S. Wei, B. Wu, Dynamic graph neural network for fake news detection, Neurocomputing, 505 (2022), 362–374. https://doi.org/10.1016/j.neucom.2022.07.057 doi: 10.1016/j.neucom.2022.07.057
|
| [5] | H. Bo, R. McConville, J. Hong, W. Liu, Social influence prediction with train and test time augmentation for graph neural networks, in Proceedings of 2021 International Joint Conference on Neural Networks (IJCNN), (2021), 1–8. https://doi.org/10.1109/IJCNN52387.2021.9533437 |
| [6] | H. Bo, R. McConville, J. Hong, W. Liu, Social network influence ranking via embedding network interactions for user recommendation, in Proceedings of WWW'20: The Web Conference, (2020), 379–384. https://doi.org/10.1145/3366424.3383299 |
| [7] |
W. Peng, J. Wang, Z. Zhang, F. X. Wu, Applications of random walk model on biological networks, Curr. Bioinf., 11 (2016), 2111–220. https://doi.org/10.2174/1574893611666160223200823 doi: 10.2174/1574893611666160223200823
|
| [8] | W. Fan, Y. Ma, Q. Li, Y. He, E. Zhao, J. Tang, et al., Graph neural networks for social recommendation, in Proceedings of WWW'19: The World Wide Web Conference, (2019), 417–426. https://doi.org/10.1145/3308558.3313488 |
| [9] | C. Huang, H. Xu, Y. Xu, P. Dai, L. Xia, M. Lu, et al., Knowledge-aware coupled graph neural network for social recommendation, in Proceedings of the AAAI Conference on Artificial Intelligence, (2021), 4115–4122. https://doi.org/10.1609/aaai.v35i5.16533 |
| [10] | C. Huang, J. Chen, L. Xia, Y. Xu, P. Dai, Y. Chen, et al., Graph-enhanced multi-task learning of multi-level transition dynamics for session-based recommendation, in Proceedings of the AAAI Conference on Artificial Intelligence, (2021), 4123–4130. https://doi.org/10.1609/aaai.v35i5.16534 |
| [11] | D. Yuxiao, N. Chawla, A. Swami, Metapath2vec: Scalable representation learning for heterogeneous networks, in KDD'17: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2017), 135–144. https://doi.org/10.1145/3097983.3098036 |
| [12] | X. Wang, H. Ji, C. Shi, B. Wang, Y. Ye, P. Cui, et al., Heterogeneous graph attention network, in Proceedings of WWW '19: The World Wide Web Conference, (2019), 2022–2032. https://doi.org/10.1145/3308558.3313562 |
| [13] | X. Fu, J. Zhang, Z. Meng, I. King, MAGNN: Metapath aggregated graph neural network for heterogeneous graph embedding, in Proceedings of WWW '20: The Web Conference, (2020), 2331–2341. https://doi.org/10.1145/3366423.3380297 |
| [14] | C. Zhang, D. Song, C. Huang, A. Swami, N. Chawla, Heterogeneous graph neural network, in KDD '19: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, (2019), 793–803. https://doi.org/10.1145/3292500.3330961 |
| [15] | C. Ying, T. Cai, S. Luo, S. Zheng, G. Ke, D. He, et al., Do transformers really perform bad for graph representation?, Adv. Neural Inf. Process. Syst., 34 (2021), 28877–28888. |
| [16] | B. Perozzi, R. Al-Rfou, S. Skiena, DeepWalk: Online learning of social representations, in Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2014), 701–710. https://doi.org/10.1145/2623330.2623732 |
| [17] | A. Grover, J. Leskovec, Node2vec: Scalable feature learning for networks, in KDD: Proceedings of International Conference on Knowledge Discovery & Data Mining, (2016), 855–864. https://doi.org/10.1145/2939672.2939754 |
| [18] | M. Defferrard, X. Bresson, P. Vandergheynst, Convolutional neural networks on graphs with fast localized spectral filtering, inProceedings of the 30th International Conference on Neural Information Processing Systems, (2016), 3844–3852. https://doi.org/10.5555/3157382.3157527 |
| [19] | P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Liò, Y. Bengio, Inductive representation learning on large graphs, in Proceedings of International Conference on Learning Representations, (2017). |
| [20] | W. Hamilton, R. Ying, J. Leskovec, Inductive representation learning on large graphs, in Proceedings of the 31st International Conference on Neural Information Processing Systems, (2017), 1025–1035. https://doi.org/10.5555/3294771.3294869 |
| [21] | T. Kipf, M. Welling, Variational graph auto-encoders, preprint, arXiv: 1611.07308. |
| [22] | A. Salehi, H. Davulcu, Graph attention auto-encoders, in Proceedings of IEEE 32nd International Conference on Tools with Artificial Intelligence (ICTAI), (2020), 989–996. https://doi.org/10.1109/ICTAI50040.2020.00154 |
| [23] | P. Veličković, W. Fedus, W. L. Hamilton, P. Liò, Y. Bengio, R. D. Hjelm, Deep Graph Infomax, in Proceedings of International Conference on Learning Representations, (2019). |
| [24] | C. Wang, S. Pan, R. Hu, G. Long, J. Jiang, C. Zhang, Attributed graph clustering: A deep attentional embedding approach, in Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19, (2019), 3670–3676. https://doi.org/10.24963/ijcai.2019/509 |
| [25] | D. Bo, X. Wang, C. Shi, M. Zhu, E. Lu, P. Cui, Structural deep clustering network, in Web Conference 2020: Proceedings of the World Wide Web Conference (WWW 2020), (2020), 1400–1410. https://doi.org/10.1145/3366423.3380214 |
| [26] | H. Liu, B. Hu, X. Wang, C. Shi, Z. Zhang, J. Zhou, Confidence may cheat: Self-training on graph neural networks under distribution shift, in Proceedings of the ACM Web Conference, (2022), 1248–1258. https://doi.org/10.1145/3485447.3512172 |
| [27] |
C. Shi, B. Hu, W. Zhao, P. Yu, Heterogeneous information network embedding for recommendation, IEEE Trans. Knowl. Data Eng., 31 (2017), 357–370. https://doi.org/10.1109/TKDE.2018.2833443 doi: 10.1109/TKDE.2018.2833443
|
| [28] | T. Fu, W. C. Lee, Z. Lei, HIN2Vec: Explore meta-paths in heterogeneous information networks for representation learning, in Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, (2017), 1797–1806. https://doi.org/10.1145/3132847.3132953 |
| [29] |
W. Wang, X. Wei, X. Suo, B. Wang, H. Wang, H. N. Dai, et al., HGATE: heterogeneous graph attention auto-encoders, IEEE Trans. Knowl. Data Eng., 35 (2021), 3938–3951. https://doi.org/10.1109/TKDE.2021.3138788 doi: 10.1109/TKDE.2021.3138788
|
| [30] | X. Fu, J. Zhang, Z. Meng, I. King, MAGNN: Metapath aggregated graph neural network for heterogeneous graph embedding, in Proceedings of The Web Conference 2020, (2020), 2331–2341. https://doi.org/10.1145/3366423.3380297 |
| [31] |
S. Zheng, D. Guan, W. Yuan, Semantic-aware heterogeneous information network embedding with incompatible meta-paths, World Wide Web, 25 (2022), 1–21. https://doi.org/10.1007/s11280-021-00903-5 doi: 10.1007/s11280-021-00903-5
|
| [32] | Y. Ren, B. Liu, C. Huang, P. Dai, L. Bo, J. Zhang, Heterogeneous deep graph infomax, preprint, arXiv: 1911.08538. |
| [33] | C. Park, D. Kim, J. Han, H. Yu, Unsupervised attributed multiplex network embedding, in Proceedings of the AAAI Conference on Artificial Intelligence, (2020), 5371–5378. |
| [34] | C. Mavromatis, G. Karypis, HeMI: Multi-view embedding in heterogeneous graphs, preprint, arXiv: 2109.07008. |
| [35] | J. Macqueen, Some methods for classification and analysis of multivariate observations, in Proceedings of Symposium on Mathematical Statistics and Probability, (1967). |
| [36] | X. Wang, N. Liu, H. Han, C. Shi, Self-supervised heterogeneous graph neural network with co-contrastive learning, in Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery Data Mining, (2021), 1726–1736. https://doi.org/10.1145/3447548.3467415 |
| [37] | Q. Zhu, W. Bi, X. Liu, X. Ma, X. Li, D. Wu, A batch normalized inference network keeps the KL vanishing away, in Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, (2020), 2636–2649. https://doi.org/10.18653/v1/2020.acl-main.235 |
| [38] | Z. Jiang, Y. Zheng, H. Tan, B. Tang, H. Zhou, Variational deep embedding: An unsupervised and generative approach to clustering, in Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, (2017), 1965–1972. https://doi.org/10.24963/ijcai.2017/273 |
| 1. | Helena Sousa, Oscar Ribeiro, Daniela Figueiredo, Purpose in life among haemodialysis caregivers: Links with adaptive coping, caregiver burden, and psychological distress, 2024, 40, 1532-3005, 10.1002/smi.3460 | |
| 2. | Edicleia Oliveira, Serge Basini, Thomas M. Cooney, Navigating gendered spaces: a feminist phenomenological exploration of women entrepreneurs lived experiences within government support agencies, 2024, 16, 1756-6266, 564, 10.1108/IJGE-10-2023-0258 | |
| 3. | Thiago Alves, Rogério S. Gonçalves, 2024, Development of a Cable-Driven Robot with a Compensation Measurement System for Bimanual and Cognitive Rehabilitation of Stroke, 1, 10.5753/sbrlars_estendido.2024.243872 | |
| 4. | Sjors F Van de Vusse, Nienke N De Laat, Lennard A Koster, Bart L Kaptein, The accuracy and precision of CT-RSA in arthroplasty: a systematic review and meta-analysis, 2025, 96, 1745-3682, 10.2340/17453674.2025.43334 | |
| 5. | Eider Arbizu Fernández, Arkaitz Galbete Jimenez, Tomás Belzunegui Otano, Mariano Fortún Moral, Alfredo Echarri Sucunza, Analysis of serious trauma injury patterns in Navarre (Spain) (2010-2019), 2024, 47, 2340-3527, 10.23938/ASSN.1085 |
Figures(6) / Tables(1)
Chuang Ma, Helong Xia. A one-step graph clustering method on heterogeneous graphs via variational graph embedding[J]. Electronic Research Archive, 2024, 32(4): 2772-2788. doi: 10.3934/era.2024125
DownLoad: