﻿ 正则化在船舶通信多维关联数据动态降维中的应用
 舰船科学技术  2022, Vol. 44 Issue (19): 150-153    DOI: 10.3404/j.issn.1672-7649.2022.19.030 PDF

1. 郑州大学，河南 郑州 450044;
2. 烟台大学，山东 烟台 264005

Application of regularization in dynamic dimensionality reduction of ship communication multidimensional linked data
DENG Feng1, CUI Zhen-dong2
1. Zhengzhou University, Zhengzhou 450044, China;
2. Yantai University, Yantai 264005, China
Abstract: The dynamic dimensionality reduction of ship communication multidimensional correlation data and the calculation idea of ship communication multidimensional correlation have brought great difficulties to its solution. According to the characteristics of ship regularization, the factors affecting the accurate solution of dynamic dimensionality reduction of ship communication data are analyzed. In order to reduce the problem of dynamic dimensionality reduction of multi-dimensional related data of ship communication, on the basis of dimensionality reduction, a multidimensional regression extension is carried out on the channel response number of the samples to improve the application of dynamic dimensionality reduction. According to practical application requirements, this paper proposes a regularization method that combines data representation and perception algorithm, which is more practical.
Key words: ship communication     data dynamics     regularization
0 引　言

1 正则化方法

1.1 TSVD
 ${\boldsymbol{A}} = {\boldsymbol{U}}\Lambda {{\boldsymbol{V}}^{\rm{T}}} = \sum\limits_{{i} = 1}^{{r}} {{{{u}}_{i}}} {\sigma _{i}}{v}_{i}^{\rm{T}} \text{，}$

 $\chi = \sum\limits_{{\text{i}} = 1}^{r} {\frac{{{{u}_{i}}{b}}}{{{\sigma _{i}}}}{\nu _{i}}} \text{，}$

A=UAvT-uov。在i=1公式中，U=[uum]及y均是正交矩阵：对角矩阵1= diag (a，0，...o)，并且O≥O，≥ O，≤0；r表示系数矩阵的秩。对于反欠问题的最小模型解，可以为x=>iov.i=1Oi，可以很容易地看出，系数矩阵的小奇异值可以被放大。为了改善求解的稳定性，TSVD的基本思路是通过对求解引起干扰的小奇异值进行截断，也就是：

 ${\chi _{TSVD}} = \sum\limits_{{\text{i}} = 1}^{k} {\frac{{{{u}_{i}}{b}}}{{{\sigma _{i}}}}{\nu _{i}}} \text{。}$

1.2 移动目标轨迹数据

 图 1 移动目标轨迹数据处理 Fig. 1 Move the target trajectory data processing

1.3 数据的表示

2 多维关联数据动态降维

 图 2 动态降维流程图 Fig. 2 Dynamic dimensionality reduction flow chart

2.1 数据降维

 $\varphi （W）=\left|\right|Tr^i-{\displaystyle \sum _{}{}_{j=1}^k}{W}_{ij}T{r}^{i}（j）|{|}^{2} \text{。}$

2.2 特征提取

2.3 船舶多维通信虚拟模型

 图 3 船舶虚拟图 Fig. 3 Ship virtual diagram

 ${\rm min}F（x）={\displaystyle \sum _{\text{r}\in R}（|{D}_{\text{r}}-\overline{D}|）} \text{。}$

1）限制1

 $\sum\limits_{{\text{r}} \in R} {{\chi _{\text{r}}} \geqslant R} \text{，}$

2） 限制2

3)极限3

 $0\leqslant {y}_{\text{i}（e）t}-{\chi }_{\text{et}}\leqslant （1-{\text{u}}_{et}）{\displaystyle \sum _{v}{\text{h}}_{vt}} \text{，}$
 ${\chi _{{\text{et}}}} \leqslant {\chi _{{\text{et}}}}\sum\limits_{n} {{{\text{h}}_{{vt}}}} \text{。}$

 ${\displaystyle \sum _{\text{r}\in R}{\chi }_{\text{r}}\leqslant {\text{v}}_{e}}（k）\text{，}{\forall }_{\text{e}} \text{。}$

 图 4 最佳数据交互波形图 Fig. 4 Best Data Interaction Waveform
3 结　语

 [1] 王宪保, 陈诗文, 姚明海. 基于正则化的半监督等距映射数据降维方法[J]. 电子与信息学报, 2016, 38(1): 5. WANG Xian-bao, CHEN Shi-wen, YAO Ming-hai. Dimensionality reduction method for semi-supervised isometric mapping data based on regularization[J]. Journal of Electronics and Information, 2016, 38(1): 5. [2] 周兴林, 王明石. 多维力传感器动态力反演正则化求解仿真[J]. 计算机仿真, 2020(037-011). ZHOU Xing-lin, WANG Ming-shi. Simulation of dynamic force inversion regularization for multi-dimensional force sensor [J]. Computer Simulation, 2020(037-011). [3] 彭艳斌, 苏先创, 邱薇薇, 等. 基于流形正则化非负矩阵分解的高光谱数据降维[J]. 光电子. 激光, 2018, 29(2): 5. PENG Yan-bin, SU Xian-chuang, QIU Wei-wei, et al. Dimensionality reduction of hyperspectral data based on manifold regularized non-negative matrix factorization[J]. Optoelectronics. Laser, 2018, 29(2): 5. [4] 朱劲夫, 刘明哲, 赵成强, 等. 正则化在逻辑回归与神经网络中的应用研究[J]. 信息技术, 2016, 40(7): 5. ZHU Jin-fu, LIU Ming-zhe, ZHAO Cheng-qiang, et al. Application of regularization in logistic regression and neural network[J]. Information Technology, 2016, 40(7): 5. DOI:10.13274/j.cnki.hdzj.2016.07.001 [5] 高云龙, 潘金艳, 陈福兴. 基于判别正则化局部保留投影的图像数据降维方法及系统: , CN111553417A[P]. 2020. GAO Yun-long, PAN Jin-yan, CHEN Fu-xing. Dimensionality Reduction Method and System for Image Data Based on Discriminant Regularization Local Preserving Projection: CN111553417A[P]. 2020. [6] 王丽艳, 李伟生. 基于判别性降维的字典学习在光照变化人脸识别中的应用[J]. 科学技术与工程, 2014(8): 7. WANG Li-yan, LI Wei-sheng. The application of dictionary learning based on discriminative dimension reduction in face recognition with illumination changes[J]. Science Technology and Engineering, 2014(8): 7. DOI:10.3969/j.issn.1671-1815.2014.08.009