{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:29:54Z","timestamp":1773239394312,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61772180"],"award-info":[{"award-number":["61772180"]}]},{"name":"National Natural Science Foundation of China","award":["2020BHB004"],"award-info":[{"award-number":["2020BHB004"]}]},{"name":"National Natural Science Foundation of China","award":["2020BAB012"],"award-info":[{"award-number":["2020BAB012"]}]},{"name":"Key R&amp;D plan of Hubei Province","award":["61772180"],"award-info":[{"award-number":["61772180"]}]},{"name":"Key R&amp;D plan of Hubei Province","award":["2020BHB004"],"award-info":[{"award-number":["2020BHB004"]}]},{"name":"Key R&amp;D plan of Hubei Province","award":["2020BAB012"],"award-info":[{"award-number":["2020BAB012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Graph neural networks have been widely used by multivariate time series-based anomaly detection algorithms to model the dependencies of system sensors. Previous studies have focused on learning the fixed dependency patterns between sensors. However, they ignore that the inter-sensor and temporal dependencies of time series are highly nonlinear and dynamic, leading to inevitable false alarms. In this paper, we propose a novel disentangled dynamic deviation transformer network (D3TN) for anomaly detection of multivariate time series, which jointly exploits multiscale dynamic inter-sensor dependencies and long-term temporal dependencies to improve the accuracy of multivariate time series prediction. Specifically, to disentangle the multiscale graph convolution, we design a novel disentangled multiscale aggregation scheme to better represent the hidden dependencies between sensors to learn fixed inter-sensor dependencies based on static topology. To capture dynamic inter-sensor dependencies determined by real-time monitoring situations and unexpected anomalies, we introduce a self-attention mechanism to model dynamic directed interactions in various potential subspaces influenced by various factors. In addition, complex temporal correlations across multiple time steps are simulated by processing the time series in parallel. Experiments on three real datasets show that the proposed D3TN significantly outperforms the state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/s23031104","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T01:33:51Z","timestamp":1674092031000},"page":"1104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Disentangled Dynamic Deviation Transformer Networks for Multivariate Time Series Anomaly Detection"],"prefix":"10.3390","volume":"23","author":[{"given":"Chunzhi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan 430068, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4786-4493","authenticated-orcid":false,"given":"Shaowen","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan 430068, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7935-7173","authenticated-orcid":false,"given":"Rong","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan 430068, China"}]},{"given":"Lingyu","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan 430068, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0394-4635","authenticated-orcid":false,"given":"Naixue","family":"Xiong","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Sul Ross State University, Alpine, TX 79830, USA"}]},{"given":"Ruoxi","family":"Wang","sequence":"additional","affiliation":[{"name":"Wuhan Fiberhome Technical Services Co., Ltd., Wuhan 430205, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1109\/TNSE.2020.3014455","article-title":"BD-VTE: A novel baseline data based verifiable trust evaluation scheme for smart network systems","volume":"8","author":"Huang","year":"2020","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cirstea, R.G., Kieu, T., Guo, C., Yang, B., and Pan, S.J. (2021, January 19\u201322). EnhanceNet: Plugin neural networks for enhancing correlated time series forecasting. Proceedings of the 2021 IEEE 37th International Conference on Data Engineering (ICDE), Chania, Greece.","DOI":"10.1109\/ICDE51399.2021.00153"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"248","DOI":"10.3390\/s150100248","article-title":"A Structure Fidelity Approach for Big Data Collection in Wireless Sensor Networks","volume":"15","author":"Wu","year":"2015","journal-title":"Sensors"},{"key":"ref_4","unstructured":"Ma, J., and Perkins, S. (2003, January 20\u201324). Time-series novelty detection using one-class support vector machines. Proceedings of the International Joint Conference on Neural Networks, Portland, OR, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1109\/TSMCA.2007.897589","article-title":"On the time series k-nearest neighbor classification of abnormal brain activity","volume":"37","author":"Chaovalitwongse","year":"2007","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kiss, I., Genge, B., Haller, P., and Sebesty\u00e9n, G. (2014, January 4\u20136). Data clustering-based anomaly detection in industrial control systems. Proceedings of the 2014 IEEE 10th International Conference on Intelligent Computer Communication and Processing (ICCP), Cluj, Romania.","DOI":"10.1109\/ICCP.2014.6937009"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hundman, K., Constantinou, V., Laporte, C., Colwell, I., and Soderstrom, T. (2018, January 19\u201323). Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, London, UK.","DOI":"10.1145\/3219819.3219845"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, D., Chen, D., Jin, B., Shi, L., Goh, J., and Ng, S.K. (2019, January 14\u201317). MAD-GAN: Multivariate anomaly detection for time series data with generative adversarial networks. Proceedings of the International Conference on Artificial Neural Networks, Bristol, UK.","DOI":"10.1007\/978-3-030-30490-4_56"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Su, Y., Zhao, Y., Niu, C., Liu, R., Sun, W., and Pei, D. (2019, January 4\u20138). Robust anomaly detection for multivariate time series through stochastic recurrent neural network. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330672"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1109\/LRA.2018.2801475","article-title":"A multimodal anomaly detector for robot-assisted feeding using an lstm-based variational autoencoder","volume":"3","author":"Park","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1991","DOI":"10.1109\/ACCESS.2018.2886457","article-title":"DeepAnT: A deep learning approach for unsupervised anomaly detection in time series","volume":"7","author":"Munir","year":"2018","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wu, Z., Pan, S., Long, G., Jiang, J., Chang, X., and Zhang, C. (2020, January 6\u201310). Connecting the dots: Multivariate time series forecasting with graph neural networks. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/3394486.3403118"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Deng, A., and Hooi, B. (2021, January 2\u20139). Graph neural network-based anomaly detection in multivariate time series. Proceedings of the AAAI Conference on Artificial Intelligence, Virtual Event.","DOI":"10.1609\/aaai.v35i5.16523"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhao, H., Wang, Y., Duan, J., Huang, C., Cao, D., Tong, Y., Xu, B., Bai, J., Tong, J., and Zhang, Q. (2020, January 17\u201320). Multivariate time-series anomaly detection via graph attention network. Proceedings of the 2020 IEEE International Conference on Data Mining (ICDM), Sorrento, Italy.","DOI":"10.1109\/ICDM50108.2020.00093"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Phiboonbanakit, T., Huynh, V.N., Horanont, T., and Supnithi, T. (2019, January 9\u201313). Detecting abnormal behavior in the transportation planning using long short term memories and a contextualized dynamic threshold. Proceedings of the Adjunct 2019 ACM International Joint Conference on Pervasive and Ubiquitous Computing and Proceedings of the 2019 ACM International Symposium on Wearable Computers, London, UK.","DOI":"10.1145\/3341162.3349324"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, Z., Zhang, H., Chen, Z., Wang, Z., and Ouyang, W. (2020, January 19\u201320). Disentangling and unifying graph convolutions for skeleton-based action recognition. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LO, USA.","DOI":"10.1109\/CVPR42600.2020.00022"},{"key":"ref_17","first-page":"5998","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1162\/neco.2007.19.7.1962","article-title":"Outliers detection in multivariate time series by independent component analysis","volume":"19","author":"Baragona","year":"2007","journal-title":"Neural Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1016\/j.camwa.2012.02.003","article-title":"Privacy-preserving max\/min query in two-tiered wireless sensor networks","volume":"65","author":"Yao","year":"2013","journal-title":"Comput. Math. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1016\/j.sysarc.2013.10.007","article-title":"Adaptive GTS allocation in IEEE 802.15. 4 for real-time wireless sensor networks","volume":"59","author":"Xia","year":"2013","journal-title":"J. Syst. Archit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TNNLS.2020.2978386","article-title":"A comprehensive survey on graph neural networks","volume":"32","author":"Wu","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gao, K., Han, F., Dong, P., Xiong, N., and Du, R. (2019). Connected Vehicle as a Mobile Sensor for Real Time Queue Length at Signalized Intersections. Sensors, 19.","DOI":"10.3390\/s19092059"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"118310","DOI":"10.1109\/ACCESS.2019.2936454","article-title":"A pedestrian detection method based on genetic algorithm for optimize XGBoost training parameters","volume":"7","author":"Jiang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Audibert, J., Michiardi, P., Guyard, F., Marti, S., and Zuluaga, M.A. (2020, January 6\u201310). Usad: Unsupervised anomaly detection on multivariate time series. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/3394486.3403392"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"58939","DOI":"10.1109\/ACCESS.2018.2866364","article-title":"Spatio-temporal vessel trajectory clustering based on data mapping and density","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Muralidhara, S., Hashmi, K.A., Pagani, A., Liwicki, M., Stricker, D., and Afzal, M.Z. (2022). Attention-Guided Disentangled Feature Aggregation for Video Object Detection. Sensors, 22.","DOI":"10.3390\/s22218583"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ma, J., Zhou, C., Yang, H., Cui, P., Wang, X., and Zhu, W. (2020, January 6\u201310). Disentangled self-supervision in sequential recommenders. Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/3394486.3403091"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, Y., Tang, S., Lei, Y., Song, W., Wang, S., and Zhang, M. (2020, January 19\u201323). Disenhan: Disentangled heterogeneous graph attention network for recommendation. Proceedings of the 29th ACM International Conference on Information & Knowledge Management, Virtual Event.","DOI":"10.1145\/3340531.3411996"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Hamaguchi, R., Sakurada, K., and Nakamura, R. (2019, January 15\u201320). Rare event detection using disentangled representation learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00955"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wang, X., Chen, H., and Zhu, W. (2021, January 5\u20139). Multimodal disentangled representation for recommendation. Proceedings of the 2021 IEEE International Conference on Multimedia and Expo (ICME), Virtual Event.","DOI":"10.1109\/ICME51207.2021.9428193"},{"key":"ref_31","unstructured":"Yamada, M., Kim, H., Miyoshi, K., Iwata, T., and Yamakawa, H. (2020, January 18\u201320). Disentangled representations for sequence data using information bottleneck principle. Proceedings of the Asian Conference on Machine Learning, PMLR, Bangkok, Thailand."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liang, J., Cao, J., Sun, G., Zhang, K., Van Gool, L., and Timofte, R. (2021, January 11\u201317). Swinir: Image restoration using swin transformer. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Montreal, BC, Canada.","DOI":"10.1109\/ICCVW54120.2021.00210"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, Q., Zhao, H., Li, W., Huang, P., and Ou, W. (2019, January 5). Behavior sequence transformer for e-commerce recommendation in alibaba. Proceedings of the 1st International Workshop on Deep Learning Practice for High-Dimensional Sparse Data, Anchorage, AL, USA.","DOI":"10.1145\/3326937.3341261"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1016\/j.ijforecast.2021.03.012","article-title":"Temporal fusion transformers for interpretable multi-horizon time series forecasting","volume":"37","author":"Lim","year":"2021","journal-title":"Int. J. Forecast."},{"key":"ref_35","unstructured":"Liu, S., Yu, H., Liao, C., Li, J., Lin, W., Liu, A.X., and Dustdar, S. (2021, January 3\u20137). Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting. Proceedings of the International Conference on Learning Representations, Virtual Event."},{"key":"ref_36","unstructured":"Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. (2014). Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Li, Z., Zhao, Y., Han, J., Su, Y., Jiao, R., Wen, X., and Pei, D. (2021, January 14\u201318). Multivariate time series anomaly detection and interpretation using hierarchical inter-metric and temporal embedding. Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, Singapore.","DOI":"10.1145\/3447548.3467075"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1186\/s13673-018-0141-x","article-title":"An energy-efficient sleep scheduling mechanism with similarity measure for wireless sensor networks","volume":"8","author":"Wan","year":"2018","journal-title":"Hum. Centric Comput. Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"7426","DOI":"10.1073\/pnas.0500334102","article-title":"Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps","volume":"102","author":"Coifman","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Li, M., Chen, S., Chen, X., Zhang, Y., Wang, Y., and Tian, Q. (2019, January 15\u201319). Actional-structural graph convolutional networks for skeleton-based action recognition. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00371"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Siffer, A., Fouque, P.A., Termier, A., and Largouet, C. (2017, January 13\u201317). Anomaly detection in streams with extreme value theory. Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Halifax, NS, Canada.","DOI":"10.1145\/3097983.3098144"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Li, J., Di, S., Shen, Y., and Chen, L. (2021, January 8\u201312). FluxEV: A fast and effective unsupervised framework for time-series anomaly detection. Proceedings of the 14th ACM International Conference on Web Search and Data Mining, Jerusalem, Israel.","DOI":"10.1145\/3437963.3441823"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ren, H., Xu, B., Wang, Y., Yi, C., Huang, C., Kou, X., Xing, T., Yang, M., Tong, J., and Zhang, Q. (2019, January 4\u20138). Time-series anomaly detection service at microsoft. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330680"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1109\/JPROC.2010.2043918","article-title":"The soil moisture active passive (SMAP) mission","volume":"98","author":"Entekhabi","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Xu, H., Chen, W., Zhao, N., Li, Z., Bu, J., Li, Z., Liu, Y., Zhao, Y., Pei, D., and Feng, Y. (2018, January 23\u201327). Unsupervised anomaly detection via variational auto-encoder for seasonal kpis in web applications. Proceedings of the 2018 World Wide Web Conference, Lyon, France.","DOI":"10.1145\/3178876.3185996"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chen, X., Deng, L., Huang, F., Zhang, C., and Zheng, K. (2021, January 19\u201322). DAEMON: Unsupervised Anomaly Detection and Interpretation for Multivariate Time Series. Proceedings of the 2021 IEEE 37th International Conference on Data Engineering (ICDE), Chania, Greece.","DOI":"10.1109\/ICDE51399.2021.00228"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"131723","DOI":"10.1109\/ACCESS.2020.3009876","article-title":"Data security and privacy protection for cloud storage: A survey","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.future.2017.07.013","article-title":"Exploring finger vein based personal authentication for secure IoT","volume":"77","author":"Lu","year":"2017","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Lu, C., Huang, J., and Huang, L. (2021). Detecting Urban Anomalies Using Factor Analysis and One Class Support Vector Machine. Comput. J.","DOI":"10.1093\/comjnl\/bxab166"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1104\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:09:01Z","timestamp":1760119741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/3\/1104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,18]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["s23031104"],"URL":"https:\/\/doi.org\/10.3390\/s23031104","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,18]]}}}