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

系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (5): 1191-1197.doi: 10.12305/j.issn.1001-506X.2021.05.05

基于双重正则矩阵分解的缺失数据恢复

刘歌*(), 芮国胜(), 田文飚()

海军航空大学, 山东烟台 264001

收稿日期:2020-05-18 出版日期:2021-05-01 发布日期:2021-04-27
通讯作者: 刘歌 E-mail:yyliuge@sina.com;ruigs@vip.sina.com;twbi5si@gmail.com
作者简介:刘歌(1991—), 女, 博士研究生, 主要研究方向为数据处理、蒸发波导反演。E-mail: yyliuge@sina.com|芮国胜(1968—), 男, 教授, 博士研究生导师, 博士, 主要研究方向为压缩感知、现代滤波理论。E-mail: ruigs@vip.sina.com|田文飚(1987—), 男, 副教授, 博士, 主要研究方向为压缩感知、蒸发波导反演。E-mail: twbi5si@gmail.com
基金资助:
国家自然科学基金(41606117);国家自然科学基金(41476089);国家自然科学基金(61671016)

Missing data recovery based on double regularization matrix decomposition

Ge LIU*(), Guosheng RUI(), Wenbiao TIAN()

Naval Aviation University, Yantai 264001, China

Received:2020-05-18 Online:2021-05-01 Published:2021-04-27
Contact: Ge LIU E-mail:yyliuge@sina.com;ruigs@vip.sina.com;twbi5si@gmail.com

摘要/Abstract

摘要：

针对多源时间序列缺失数据恢复问题, 提出一种基于双重正则矩阵分解的恢复方法。该方法在多源时间序列矩阵分解的基础上, 利用时间序列的平滑性构建时间序列隐含因子的二阶差分正则项, 同时引入反映数据内部结构的图拉普拉斯正则项对传感器隐含因子进行约束, 并在图拉普拉斯矩阵获取过程中设计了一种联合数据本身的相似度和数据变化趋势相似度的双重皮尔逊相似策略, 构造数据内部的最相似图。最后，将双正则项统一于矩阵分解的框架中, 利用梯度下降法实现目标函数的优化, 数据实验中分别采用合成数据和真实数据验证了算法的有效性。

关键词: 多源时间序列, 数据缺失, 矩阵分解, 图拉普拉斯正则化

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

中图分类号:

TN911.73

刘歌, 芮国胜, 田文飚. 基于双重正则矩阵分解的缺失数据恢复[J]. 系统工程与电子技术, 2021, 43(5): 1191-1197.

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.

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参考文献 18

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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

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基于双重正则矩阵分解的缺失数据恢复

Missing data recovery based on double regularization matrix decomposition

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