基于双重正则矩阵分解的缺失数据恢复

doi:10.12305/j.issn.1001-506X.2021.05.05

Abstract

Abstract:

In order to recover the missing data of multi-source time series, a recovery method based on double regular matrix decomposition is proposed. Based on the matrix decomposition of multi-source time series, the second-order difference normal term of hidden factor of time series is constructed by using the smoothness of time series. Meanwhile, the hidden cause of sensor is introduced by the regular term of graph Laplacian which reflects the internal structure of data. In order to construct the most similar graph in the data, a double Pearson similarity strategy combining the similarity of data itself and the similarity of data change trend is designed in the process of obtaining the matrix, and the comprehensive correlation coefficient is calculated by the Euclidean distance method. Finally, the double regular terms are unified in the framework of matrix decomposition and realized by the gradient descent method. Through the optimization of the objective function, high recovery performance can be obtained. The effectiveness of the algorithm is proved by theoretical analysis and simulation experiments.

Key words: multi-source time series, data missing, matrix decomposition, graph Laplacian regularization

CLC Number:

TN911.73

Ge LIU, Guosheng RUI, Wenbiao TIAN. Missing data recovery based on double regularization matrix decomposition[J]. Systems Engineering and Electronics, 2021, 43(5): 1191-1197.

Figures/Tables 5

Fig.1

Fig.2

Table 1

Fig.3

Table 2

References 18

1	孙利民, 李建中, 陈渝, 等. 无线传感器网络[M]. 北京: 清华大学出版社, 2008.
	SUN L M , LI J Z , CHEN Y , et al. Wireless sensor networks[M]. Beijing: Tsinghua University Press, 2008.
2	杨坤德, 马远良, 史阳. 西太平洋蒸发波导的时空统计规律研究[J]. 物理学报, 2009, 58 (10): 7339- 7350.
	YANG K D , MA Y L , SHI Y . Spatio-temporal distributions of evaporation duct for the West Pacific Ocean[J]. Acta Physica Sinica, 2009, 58 (10): 7339- 7350.
3	LIANG T , YUAN Y J . Wearable medical monitoring systems based on wireless networks: a review[J]. Sensors Journal IEEE, 2016, 16 (23): 8186- 8199.
4	QIAN C C , LIU A C , HUANG R , et al. Quality control of marine big data: a case study of real-time observation station data in Qingdao[J]. Journal of Oceanology & Limnology, 2019, 37 (6): 1983- 1993. doi: 10.1007/s00343-019-8258-y
5	陈伟彪, 陈亦平, 姚伟, 等. 基于多源信息时间序列匹配的电网故障诊断方法[J]. 电力建设, 2016, 37 (12): 134- 142.
	CHEN W B , CHEN Y P , YAO W , et al. Fault diagnosis method of power grid based on time series matching with multi-source information[J]. Electric Power Construction, 2016, 37 (12): 134- 142.
6	FOUAD H , MAHMOUD N M , MOHAMMED S I , et al. Distributed and scalable computing framework for improving request processing of wearable IoT assisted medical sensors on pervasive computing system[J]. Computer Communications, 2020, 151, 257- 265. doi: 10.1016/j.comcom.2020.01.020
7	YANG G X, LIU Z. The design of forest fire monitoring system based on wireless sensor network[C]//Proc. of the IET International Forum on Strategic Technology, 2013.
8	CHUAN Z L , DENI S M , FAM S F , et al. The effectiveness of a probabilistic principal component analysis model and expectation maximization algorithm in treating missing daily rainfall data[J]. Asia-Pacific Journal of Atmospheric Sciences, 2020, 56, 119- 129. doi: 10.1007/s13143-019-00135-8
9	KOZERA R, WILKO AZKA M. Natural spline interpolation and exponential parameterization for length estimation of curves[C]//Proc. of the International Conference of Numerical Analysis & Applied Mathematics, 2016: 19-25.
10	LIPPI M , BERTINI M , FRASCONI P . Short-term traffic flow forecasting: an experimental comparison of time-series analysis and supervised learning[J]. IEEE Trans.on Intelligent Transportation Systems, 2013, 14 (2): 871- 882. doi: 10.1109/TITS.2013.2247040
11	LUCIA P M , GIUSEPPINA A , MICHELE L , et al. Reconstructing missing data sequences in multivariate time series: an application to environmental data[J]. Statistical Methods & Applications, 2019, 28, 359- 383.
12	CAI J F , CANDES E J , SHEN Z W . A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20 (4): 1956- 1982. doi: 10.1137/080738970
13	JAIN P, MEKA R, DHILLON I. Guaranteed rank minimization via singular value projection[C]//Proc. of the Advances in 23rd International Conference on Neural Information Processing Systems, 2010: 937-945.
14	WANG N , YAO T , WANG J , et al. A probabilistic approach to robust matrix factorization[J]. Lecture Notes in Computer Science, 2012, 7578 (7): 126- 139.
15	SONG Y, LIU M, TANG S, et al. Time series matrix factorization prediction of internet traffic matrices[C]//Proc. of the IEEE Conference on Local Computer Networks, 2012: 284-287.
16	SHI W W , ZHU Y X , PHILIP S , et al. Effective prediction of missing data on apache spark over multivariable time series[J]. IEEE Trans.on Big Data, 2018, 4 (4): 493- 486.
17	BELKIN M , NIYOGI P . Laplacian eigenmaps and spectral techniques for embedding and clustering[J]. Advances in Neural Information Processing Systems, 2002, 14 (6): 585- 591.
18	CAI D, WANG X H, HE X F. Probabilistic dyadic data analysis with local and global consistency[C]//Proc. of the International Conference on Machine Learning, 2009: 105-112.

数据集	r	α	γ	c
SYN	18	0.9	0.07	0.9
ME	4	1	0.06	0.85
Motes	12	0.6	0.12	0.8

数据集	SVP	GSDAM	TDMF	MF	DRMF
Motes	3.678 6	10.948 6	3.826 4	0.270 6	0.528 1
SYN	2.474 0	15.583 9	4.246 7	0.530 9	3.142 2
ME	2.141 0	14.940 6	4.902 3	0.580 5	2.658 1

[1]	SUN Haiwen, XIE Xiaofang, SUN Tao, ZHANG Longjie. Threat assessment method of warships formation air defense based on DBN under the condition of small sample data missing [J]. Systems Engineering and Electronics, 2019, 41(6): 1300-1308.
[2]	WU Huali, XIAO Zhicai, ZHOU Dawang, WANG Lingling. SINS installation error matrix decoupling method based on matrix decomposition [J]. Systems Engineering and Electronics, 2018, 40(5): 1091-1097.
[3]	REN Jia, GAO Xiao-guang, RU Wei. Parameter learning of discrete dynamic Bayesian network with missing target data [J]. Journal of Systems Engineering and Electronics, 2011, 33(8): 1885-1890.

Missing data recovery based on double regularization matrix decomposition

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 5

References 18

Related Articles 3

Recommended Articles

Metrics

Comments