Anomaly Detection of Multivariate Time Series Based on Riemannian Manifolds_Journal of Biomedical Engineering

Authors：

 XUYonghong , HOUXiaoying , LIShuting , CUIJie

Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China;

Corresponding author：

XUYonghong, Email: xyh@ysu.edu.cn

Keywords：

anomaly detection; covariance matrix; Riemannian manifold; statistical process control chart

DOI：

10.7507/1001-5515.20150099

Video：

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Abstract Full text Figures/Tables Video References Cited by

Multivariate time series problems widely exist in production and life in the society. Anomaly detection has provided people with a lot of valuable information in financial, hydrological, meteorological fields, and the research areas of earthquake, video surveillance, medicine and others. In order to quickly and efficiently find exceptions in time sequence so that it can be presented in front of people in an intuitive way, we in this study combined the Riemannian manifold with statistical process control charts, based on sliding window, with a description of the covariance matrix as the time sequence, to achieve the multivariate time series of anomaly detection and its visualization. We made MA analog data flow and abnormal electrocardiogram data from MIT-BIH as experimental objects, and verified the anomaly detection method. The results showed that the method was reasonable and effective.

Citation： XUYonghong, HOUXiaoying, LIShuting, CUIJie. Anomaly Detection of Multivariate Time Series Based on Riemannian Manifolds. Journal of Biomedical Engineering, 2015, 32(3): 542-547. doi: 10.7507/1001-5515.20150099 Copy

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7.	郝井华, 刘民, 吴澄, 等.一种基于LLM的高维时间序列数据异常检测方法[J].控制工程, 2005, 12(3):207-209, 265.
8.	TOKUDA T, GOODRICH B, VAN MECHELEN I, et al. Visualizing distributions of covariance matrices[R].University of Leuwen, Belgium and Columbia University, 2011.
9.	HUANG A, WAND M P. Simple marginally noninformative prior distributions for covariance matrices[J]. Bayesian Analysis, 2013, 8(2):439-452.
10.	DANIELS M J. Computing posterior distributions for covariance matrices[J]. Computing Science and Statistics, 1998:192-196.
11.	BARACHANT A, BONNET S, CONGEDO M, et al. A Brain-Switch using riemannian geometry[C]//Proceedings of the 5th International BCI Conference 2011, Austria:2011:64-67.
12.	BARACHANT A, BONNET S, CONGEDO M, et al. Common spatial pattern revisited by riemannian geometry[C]//2010 IEEE International Workshop on Multimedia Signal Processing (MMSP). Saint-Malo:2010:472-476.
13.	BARACHANT A, ANDREEV A, CONGEDO M. The riemannian potato:an automatic and adaptive artifact detection method for online experiments using riemannian geometry[C]//TOBI Workshop lV. 2013. Sion:2013:19-20.
14.	FÖRSTNER W, MOONEN B. A metric for covariance matrices[J]. Quo Vadis Geodesia, 1999:113-128.
15.	王翔宇, 张引琼.基于MATLAB的时间序列异常检测方法探讨[J].电脑知识与技术, 2012, 8(4):866-872.
16.	MABOUDOU-TCHAO E M, AGBOTO V. Monitoring the covariance matrix with fewer observations than variables[J].Computational Statistcs and Data Analysis, 2013:99-112.
17.	MABOUDOU-TCHAO E M, DIAWARA N. A LASSO chart for monitoring the covariance matrix[J]. Quality Technology and Quantitative Management, 2013, 10(1):95-114.
18.	HAWKINS D M, MABOUDOU-TCHAO E M. Multivariate exponentially weighted moving covariance matrix[J]. Technometrics, 2008, 50(2):155-166.

1. CHANDOLA V, BANERJEE A, KUMAR V. Anomaly detection:a survey[J]. ACM Computing Surveys(CSUR), 2009, 41(3):15.
2. POVINELLI R J, FENG X. A new temporal pattern identification method for characterization and prediction of complex time series events[J].IEEE Transactions on Knowledge and Data Engineering, 2003, 15(2):339-352.
3. PAPADIMITRIOU S, SUN J, FALOUTSOS C. Streaming pattern discovery in multiple time-series[C]//Proceedings of the 31st international conference on Very large data bases. VLDB Endowment, Trondheim:2005:697-708.
4. BREUNIG M M, KRIEGEL H P, NG R T, et al. LOF:identifying density-based local outliers[C]//ACM Sigmod Record. Dallas:2000:93-104.
5. 王欣.两阶段的多元时间序列异常检测算法[J].计算机应用研究, 2011, 28(7):2466-2469.
6. 李权, 周兴社.一种新的多变量时间序列数据异常检测方法[J].时间频率学报, 2011, 34(2):154-158.
7. 郝井华, 刘民, 吴澄, 等.一种基于LLM的高维时间序列数据异常检测方法[J].控制工程, 2005, 12(3):207-209, 265.
8. TOKUDA T, GOODRICH B, VAN MECHELEN I, et al. Visualizing distributions of covariance matrices[R].University of Leuwen, Belgium and Columbia University, 2011.
9. HUANG A, WAND M P. Simple marginally noninformative prior distributions for covariance matrices[J]. Bayesian Analysis, 2013, 8(2):439-452.
10. DANIELS M J. Computing posterior distributions for covariance matrices[J]. Computing Science and Statistics, 1998:192-196.
11. BARACHANT A, BONNET S, CONGEDO M, et al. A Brain-Switch using riemannian geometry[C]//Proceedings of the 5th International BCI Conference 2011, Austria:2011:64-67.
12. BARACHANT A, BONNET S, CONGEDO M, et al. Common spatial pattern revisited by riemannian geometry[C]//2010 IEEE International Workshop on Multimedia Signal Processing (MMSP). Saint-Malo:2010:472-476.
13. BARACHANT A, ANDREEV A, CONGEDO M. The riemannian potato:an automatic and adaptive artifact detection method for online experiments using riemannian geometry[C]//TOBI Workshop lV. 2013. Sion:2013:19-20.
14. FÖRSTNER W, MOONEN B. A metric for covariance matrices[J]. Quo Vadis Geodesia, 1999:113-128.
15. 王翔宇, 张引琼.基于MATLAB的时间序列异常检测方法探讨[J].电脑知识与技术, 2012, 8(4):866-872.
16. MABOUDOU-TCHAO E M, AGBOTO V. Monitoring the covariance matrix with fewer observations than variables[J].Computational Statistcs and Data Analysis, 2013:99-112.
17. MABOUDOU-TCHAO E M, DIAWARA N. A LASSO chart for monitoring the covariance matrix[J]. Quality Technology and Quantitative Management, 2013, 10(1):95-114.
18. HAWKINS D M, MABOUDOU-TCHAO E M. Multivariate exponentially weighted moving covariance matrix[J]. Technometrics, 2008, 50(2):155-166.

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