一种快速的多个主成分并行提取算法

孔令智; 高迎彬; 李红增; 张华鹏

doi:10.16383/j.aas.2017.c160299

一种快速的多个主成分并行提取算法

doi: 10.16383/j.aas.2017.c160299

孔令智^1,,
高迎彬^2,3, ,,
李红增^2,,
张华鹏^3,

1.
北京交通大学电子信息工程学院北京 100044
2.
火箭军工程大学西安 710025
3.
火箭军驻石家庄地区军事代表室石家庄 050081

基金项目:

陕西省自然科学基金 2016JM6015

国家自然科学基金 61374120

国家自然科学基金 61673387

详细信息

作者简介:
孔令智  北京交通大学硕士研究生.主要研究方向为网络安全和故障诊断.E-mail:bjtuklz@bjtu.edu.cn

李红增  火箭军工程大学讲师.主要研究方向为自适应信号处理和故障诊断.E-mail:realwar2003@163.com

张华鹏  火箭军驻石家庄地区军代室工程师.主要研究方向为数字通信.E-mail:potzhp@126.com

通讯作者:
高迎彬火箭军工程大学博士研究生.主要研究方向为信号处理和神经网络.E-mail:welcome8793@sina.com

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出版历程
- 收稿日期: 2016-04-06
- 录用日期: 2016-08-31
- 刊出日期: 2017-05-01

A Fast Algorithm That Extracts Multiple Principle Components in Parallel

1.
School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044
2.
The Rocket Force University of Engineering, Xi'an 710025
3.
The Military Deputy Office of the Rocket Force in Shijiazhuang, Shijiazhuang 050081

Funds:

Natural Science Foundation of Shaanxi Province 2016JM6015

National Natural Science Foundation of China 61374120

National Natural Science Foundation of China 61673387

More Information

Author Bio:
Master student at the School of Electronic and Information Engineering, Beijing Jiaotong University. Her research interest covers network security and fault diagnosis

Lecturer at The Rocket Force University of Engineering. His research interest covers adaptive signal processing and fault diagnosis

Engineer at The Military Deputy Office of the Rocket Force in Shijiazhuang. His main research interest is digital communication

Corresponding author: GAO Ying-Bin Ph.D. candidate at the Rocket Force University of Engineering. His research interest covers signal processing and neural networks. Corresponding author of this paper.

摘要

摘要: 主成分分析是信号处理和数据统计领域内非常重要的分析工具.针对现有多个主成分提取算法收敛速度慢的问题，提出了具有快速收敛速度的神经网络算法.该算法能够并行提取信号中的多个主成分，而不需要其他额外的操作.分别采用平稳点分析法和随机离散时间分析法对所提算法的收敛性和自稳定性进行了证明.仿真实验表明，相比现有算法，所提算法不仅具有较快的收敛速度，而且具有较高的收敛精度.
- 主成分分析 /
- 并行提取 /
- 自稳定性 /
- 神经网络
Abstract: Principle component analysis is a powerful tool in signal processing and data analysis. Up to now, some existing algorithms for multiple principal components extraction have a slow convergence speed. In order to solve this problem, a faster convergence algorithm is proposed, which can extract multiple principal components from the input signal in parallel. The equilibrium point analysis method and stochastic discrete time method are adopted to analyze the convergence and self-stabilizing property of the proposed algorithm. Simulation results show that compared with some existing algorithms, the proposed algorithm not only has a faster convergence speed but also has a higher estimating accuracy.
- Principle component analysis /
- extraction in parallel /
- self-stabilizing property /
- neural networks

HTML全文

图 1 FMPCE算法的方向余弦曲线

Fig. 1 DC curves of FMPCE

下载: 全尺寸图片幻灯片

图 2 FMPCE算法的权向量模值曲线

Fig. 2 Norm curves of FMPCE

下载: 全尺寸图片幻灯片

图 3 不同初始条件下FMPCE算法的权矩阵模值曲线

Fig. 3 Norm curves of FMPCE under different conditions

下载: 全尺寸图片幻灯片

图 4 三种算法提取第一个主成分的方向余弦曲线

Fig. 4 DC curves of three algorithms for the 1st PC

下载: 全尺寸图片幻灯片

图 5 三种算法提取第二个主成分的方向余弦曲线

Fig. 5 DC curves of three algorithms for the 2nd PC

下载: 全尺寸图片幻灯片

图 6 原始的与重构后的Lena图像

Fig. 6 Original and reconstituted Lena images

下载: 全尺寸图片幻灯片

表 1 不同重构维数下三种算法的重构误差

Table 1 Reconstitution errors of the three algorithms with different reconstitution dimensions

重构维数	1	4	7
FMPCE	0.094	0.0837	0.0813
MED-GOPAST	0.0959	0.0852	0.0846
MNIC	0.1283	0.1015	0.0933

下载: 导出CSV

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