基于低秩张量完备的电磁大数据标注补全算法

doi:10.12305/j.issn.1001-506X.2024.02.02

摘要/Abstract

摘要：

全面、准确的电磁数据标注是电磁大数据智能分析的前提和基础。针对战场博弈强对抗条件下电磁感知数据存在的标注率低、标注信息错误冗余等问题, 提出基于张量完备理论的标注补全方案。理论上, 同一场景下的同一目标, 利用不同感知平台观测提取的特征参数(如雷达脉冲参数)是相似(低秩)的, 且在一段观测时间内的测量结果是分段连续光滑的。故跨平台接收的目标数据标注补全可以建模为基于低秩张量完备的特征复原模型, 并引入全变分正则来刻画一段时间内特征参数的分段连续光滑属性。由于模型非凸, 使用基于矩阵最大秩分解的非凸近似算法进行迭代求解。通过仿真数据以及雷达脉冲描述字实侦数据并对模型的性能进行测试。实验结果表明, 所提方法在目标特征标注信息严重缺失的情况下能够很好地实现标注补全, 同时具有一定的标注纠错功能。

关键词: 标注补全, 电磁大数据, 低秩矩阵恢复

Abstract:

Comprehensive and accurate labeling of electromagnetic data is the prerequisite and foundation for intelligent analysis of electromagnetic big data. Aiming at the problems of low labeling rate and error redundant labeling information in electromagnetic sensing data under the condition of strong confrontation in battlefield games, an annotation and completion scheme based on tensor completeness theory is proposed. Theoretically, the feature parameters (such as radar pulse parameters) extracted from the observation of the same target using different sensing platforms in the same scene are similar (low-rank), and the measurement results over a period of observation time are piece-wise continuous and smooth. Therefore, the annotation and completion of target data received across platforms can be modeled as a feature restoration model based on low rank tensor completeness, and total variation regularization is introduced to characterize the piece-wise continuous smooth attributes of feature parameters over a period of time. Because the model is non-convex, a non-convex approximation algorithm based on the maximum rank decomposition of the matrix is used for iterative solution. The performance of the model is tested through simulation data and radar pulse description word (PDW) real detection data. The experimental results show that the proposed method can well achieve annotation and completion in the case of severe lack of target feature annotation information, and correct annotation errors efficiently.

Key words: annotation and completion, electromagnetic big data, low-rank tensor completion

中图分类号:

TN911.7

孙国敏, 张伟, 邵怀宗, 方旖, 李鹏飞. 基于低秩张量完备的电磁大数据标注补全算法[J]. 系统工程与电子技术, 2024, 46(2): 381-390.

Guomin SUN, Wei ZHANG, Huaizong SHAO, Yi FANG, Pengfei LI. A low-rank tensor completion based method for electromagnetic big data annotation recovery[J]. Systems Engineering and Electronics, 2024, 46(2): 381-390.

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参考文献 30

1	何友, 朱扬勇, 赵鹏, 等. 国防大数据概述[J]. 系统工程与电子技术, 2016, 38 (6): 1300- 1305.
	HE Y , ZHU Y Y , ZHAO P , et al. Panorama of national defense big data[J]. Systems Engineering and Electronics, 2016, 38 (6): 1300- 1305.
2	LI A , ZANG Q , SUN D , et al. A text feature-based approach for literature mining of IncRNA-protein interactions[J]. Neurocomputing, 2016, (7): 1417- 1421.
3	ARLOTTA L, CRESCENZ V, MECCA G, et al. Automatic annotation of data extracted from large web sites[C]//Proc. of the 6th International Workshop on Web and Databases, 2003: 7-12.
4	李明, 李秀兰. 基于结果模式的Deep Web数据标注方法[J]. 计算机应用, 2011, 31 (7): 1733- 1736.
	LI M , LI X L . Deep web data annotation method based on result schema[J]. Journal of Computer Application, 2011, 31 (7): 1733- 1736.
5	CHEN Y D, XU H, CARAMANIS C, et al. Robust matrix completion and corrupted columns[C]//Proc. of the 28th International Conference on Machine Learning, 2011: 873-880.
6	NEGAHBAN S , WAIN M J . Restricted strong convexity and weighted matrix completion: optimal bounds with noise[J]. Journal of Machine Learning Research, 2012, 5 (13): 1665- 1697.
7	DAI W , KERM E , MILENK O . A geometric approach to low-rank matrix completion[J]. IEEE Trans. on Information Theory, 2012, 58 (1): 237- 247. doi: 10.1109/TIT.2011.2171521
8	白宏阳, 马军勇, 熊凯, 等. 图像修复中的加权矩阵补全模型设计[J]. 系统工程与电子技术, 2016, 38 (7): 1703- 1708.
	BAI H Y , MA J Y , XIONG K , et al. Design of weighted matrix completion model in image inpainting[J]. Systems Engineering and Electronics, 2016, 38 (7): 1703- 1708.
9	ZHUANG L S , ZHOU Z H , GAO S H , et al. Label information guided graph construction for semi-supervised learning[J]. IEEE Trans. on Image Processing, 2017, 26 (9): 4182- 4192. doi: 10.1109/TIP.2017.2703120
10	LI B Z , ZHAO X L , ZHANG X J , et al. A learnable group-tube transform induced tensor nuclear norm and its application for tensor completion[J]. SIAM Journal on Imaging Sciences, 2023, 16 (3): 1370- 1397. doi: 10.1137/22M1531907
11	TANG X L, ZHAO X L, LIU J, et al. Uncertainty-aware unsupervised image deblurring with deep residual prior[C]//Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, 2023.
12	WANG J L, HUANG T Z, ZHAO X L, et al. CoNoT: coupled nonlinear transform based low-rank tensor representation for multi-dimensional visual data completion[EB/OL]. [2023-03-28]. DOI: 10.1109/tnnls.2022.3217198.
13	LI B Z , ZHAO X L , JI T Y , et al. Nonlinear transform based tensor nuclear norm for low-rank tensor completion[J]. Journal of Scientific Computing, 2023, 92, 83.
14	LUO Y S , ZHAO X L , JIANG T X , et al. Self-supervised nonlinear transform-based tensor nuclear norm for multi-dimensional image recovery[J]. IEEE Trans. on Image Processing, 2022, 31, 3793- 3808. doi: 10.1109/TIP.2022.3176220
15	DING M , HUANG T Z , ZHAO X L , et al. Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence[J]. Signal Processing, 2022, 194, 194- 208.
16	LI B Z , ZHAO X L , WANG J L , et al. Tensor completion via collaborative sparse and low-rank transforms[J]. IEEE Trans. on Computational Imaging, 2021, 7, 1289- 1303. doi: 10.1109/TCI.2021.3126232
17	ZHEN Y B, HUANG T Z, ZHAO X L, et al. Fully-connected tensor network decomposition and its application to higher-order tensor completion[C]//Proc. of the 35th AAAI Conference on Artificial Intelligence, 2021: 11071-11078.
18	WEN H X , ZHAO X L , JIANG T X , et al. Deep plug-and-play prior for low-rank tensor completion[J]. Neurocomputing, 2020, 400, 137- 149. doi: 10.1016/j.neucom.2020.03.018
19	赵洪山, 寿佩瑶, 马利波. 低压台区缺失数据的张量补全方法[J]. 中国电机工程学报, 2020, 40 (22): 7328- 7337.
	ZHAO H S , SHOU P Y , MA L B . A Tensor completion method of missing data in transformer district[J]. Proceedings of the CSEE, 2020, 40 (22): 7328- 7337.
20	LI X P , CHEUNG S H . Robust low-rank tensor completion based on tensor ring rank via ellnorm[J]. IEEE Trans. on Signal Processing, 2021, 69, 3685- 3698. doi: 10.1109/TSP.2021.3085116
21	ZHOU P L , LIN C Y , ZHOU C , et al. Tensor factorization for low-rank tensor completion[J]. IEEE Trans. on Image Processing, 2018, 27 (3): 1152- 1163. doi: 10.1109/TIP.2017.2762595
22	B AI , Y Q . Nonconvex tensor relative total variation for image completion[J]. Mathematics, 2023, 11 (7): 1682- 1699. doi: 10.3390/math11071682
23	KESHAVAN A H , MONTANARI A , OH S . Matrix completion from noisy entries[J]. Journal of Machine Learning Research, 2010, 11 (3): 2057- 2078.
24	RECHT B . Simpler approach to matrix completion[J]. Journal of Machine Learning Research, 2011, 12 (7): 3413- 3430.
25	CANDES E J , PLAN Y . Matrix completion with noise[J]. Proc.of the IEEE, 2010, 98 (6): 925- 936. doi: 10.1109/JPROC.2009.2035722
26	王彩云, 赵焕玥, 王佳宁, 等. 快速加权核范数最小化的SAR图像去噪算法[J]. 系统工程与电子技术, 2019, 41 (7): 1504- 1508.
	WANG C Y , ZHAO H Y , WANG J N , et al. SAR image denoising via fast weighted nuclear norm minimization[J]. Systems Engineering and Electronics, 2019, 41 (7): 1504- 1508.
27	HESTENES M . Multiplier and gradient methods[J]. Journal of Optimization Theory and Applications, 1969, 4, 303- 320. doi: 10.1007/BF00927673
28	JI T Y , HUANG T Z , ZHAO X L , et al. Tensor completion using total variation and low-rank matrix factorization[J]. Information Sciences, 2016, 326, 243- 257. doi: 10.1016/j.ins.2015.07.049
29	TOH K C , YUN S . An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems[J]. Pacific Journal of Optimization, 2010, 6 (3): 615- 640.
30	ZHANG W , YANG J , LI Q , et al. Cooperative electromagnetic data annotation via low-rank matrix completion[J]. Remote Sensing, 2023, 15 (1): 121- 130.

标注时刻	平台序号	目标序号	标注信息
标注时刻	平台序号	目标序号	时间	经度	纬度	海拔	频段	强度	…
t_i	1	1	××	××	××	××	××	××	…
									…
		n	××	××	××	××	××	××	…
		…							…
	m	1	××	××	××	××	××	××	…
		…							…
		n	××	××	××	××	××	××	…

序号	列序号
序号	1	2	3	4	5
1	0.605 63	0.562 11	0.614 87	0.621 79	0.621 90
2	0.607 62	0.591 46	0.596 92	0.624 76	0.611 59
3	0.580 36	0.66 73	0.608 51	0.612 82	0.560 10
4	0.597 56	0.616 82	0.612 46	0.658 91	0.576 56
5	0.599 11	0.577 54	0.572 07	0.613 90	0.618 08
6	0.614 58	0.612 74	0.609 07	0.592 47	0.666 69
7	0.604 17	0.602 26	0.604 20	0.615 27	0.638 70
8	0.661 89	0.580 28	0.607 95	0.595 76	0.651 27
9	0.650 88	0.639 17	0.651 12	0.570 91	0.600 10
10	0.586 72	0.659 89	0.564 41	0.652 66	0.561 41

序号	列序号
序号	1	2	3	4	5
1	0.605 63	0.562 11	0	0	0.621 90
2	0.607 62	0.591 46	0.596 92	0.624 76	0
3	0.580 36	0.667 30	0	0.612 82	0.560 10
4	0.597 56	0.616 82	0	0.658 91	0.576 56
5	0	0.577 54	0.572 07	0.613 90	0
6	0.614 58	0	0	0.592 47	0.666 69
7	0.604 17	0	0	0	0.638 70
8	0.661 89	0.580 28	0	0.595 76	0.651 27
9	0.650 88	0.639 17	0.651 12	0.570 91	0
10	0.586 72	0.659 89	0.564 41	0.652 66	0.561 41

序号	列序号
序号	1	2	3	4	5
1	0.605 63	0.562 11	0.614 87	0.621 79	0.621 90
2	0.607 62	0.591 46	0.596 92	0.624 76	0.611 59
3	0.580 36	0.667 30	0.608 51	0.612 82	0.560 10
4	0.597 56	0.616 82	0.612 46	0.658 91	0.576 56
5	0.599 11	0.577 54	0.572 07	0.613 90	0.618 08
6	0.614 58	0.612 74	0.609 07	0.592 47	0.666 69
7	0.604 17	0.602 26	0.604 20	0.615 27	0.638 70
8	0.661 89	0.580 28	0.607 95	0.595 76	0.651 27
9	0.650 88	0.639 17	0.651 12	0.570 91	0.600 10
10	0.586 72	0.659 89	0.564 41	0.652 66	0.561 41

序号	列序号
序号	1	2	3	4	5
1	0.605 63	0.562 11	0.594 83	0.617 11	0.621 90
2	0.607 62	0.591 46	0.596 92	0.624 76	0.611 59
3	0.580 36	0.667 30	0.620 17	0.612 82	0.560 10
4	0.597 56	0.616 82	0.609 59	0.658 91	0.576 56
5	0.592 87	0.577 54	0.572 07	0.613 90	0.604 18
6	0.614 58	0.607 41	0.602 28	0.592 47	0.666 69
7	0.604 17	0.599 34	0.611 75	0.605 28	0.638 70
8	0.661 89	0.580 28	0.620 13	0.595 76	0.651 27
9	0.650 88	0.639 17	0.651 12	0.570 91	0.621 17
10	0.586 72	0.659 89	0.564 41	0.652 66	0.561 41