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

计量
- 文章访问数: 2683
- HTML全文浏览量: 361
- PDF下载量: 731
- 被引次数: 0
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

参考文献(22)

[1]	Kong X Y, Hu C H, Ma H G, Han C Z. A unified self-stabilizing neural network algorithm for principal and minor components extraction. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(2): 185-198 doi: 10.1109/TNNLS.2011.2178564
[2]	李伟, 焦松, 陆凌云, 杨明.基于特征差异的仿真模型验证及选择方法.自动化学报, 2014, 40(10): 2134-2144 http://www.aas.net.cn/CN/abstract/abstract18488.shtml Li Wei, Jiao Song, Lu Ling-Yun, Yang Ming. Validation and selection of simulation model based on the feature differences. Acta Automatica Sinica, 2014, 40(10): 2134-2144 http://www.aas.net.cn/CN/abstract/abstract18488.shtml
[3]	潘宗序, 禹晶, 肖创柏, 孙卫东.基于光谱相似性的高光谱图像超分辨率算法.自动化学报, 2014, 40(12): 2797-2807 http://www.aas.net.cn/CN/abstract/abstract18558.shtml Pan Zong-Xu, Yu Jing, Xiao Chuang-Bai, Sun Wei-Dong. Spectral similarity-based super resolution for hyperspectral images. Acta Automatica Sinica, 2014, 40(12): 2797-2807 http://www.aas.net.cn/CN/abstract/abstract18558.shtml
[4]	樊继聪, 王友清, 秦泗钊.联合指标独立成分分析在多变量过程故障诊断中的应用.自动化学报, 2013, 39(5): 494-501 http://www.aas.net.cn/CN/abstract/abstract17927.shtml Fan Ji-Cong, Wang You-Qing, Qin S J. Combined indices for ICA and their applications to multivariate process fault diagnosis. Acta Automatica Sinica, 2013, 39(5): 494-501 http://www.aas.net.cn/CN/abstract/abstract17927.shtml
[5]	高全学, 高菲菲, 郝秀娟, 程洁.基于图像欧氏距离的二维局部多样性保持投影.自动化学报, 2013, 39(7): 1062-1070 http://www.aas.net.cn/CN/abstract/abstract18134.shtml Gao Quan-Xue, Gao Fei-Fei, Hao Xiu-Juan, Cheng Jie. Image Euclidean distance-based two-dimensional local diversity preserving projection. Acta Automatica Sinica, 2013, 39(7): 1062-1070 http://www.aas.net.cn/CN/abstract/abstract18134.shtml
[6]	Oja E. A simplified neuron model as a principal component analyzer. Journal of Mathematical Biology, 1982, 15(3): 267-273 doi: 10.1007/BF00275687
[7]	Miao Y F, Hua Y B. Fast subspace tracking and neural network learning by a novel information criterion. IEEE Transactions on Signal Processing, 1998, 46(7): 1967-1979 doi: 10.1109/78.700968
[8]	Peng D Z, Yi Z, Xiang Y. A unified learning algorithm to extract principal and minor components. Digital Signal Processing, 2009, 19(4): 640-649 doi: 10.1016/j.dsp.2009.03.004
[9]	Kong X Y, Hu C H, Han C Z. A dual purpose principal and minor subspace gradient flow. IEEE Transactions on Signal Processing, 2012, 60(1): 197-210 doi: 10.1109/TSP.2011.2169060
[10]	Ouyang S, Bao Z. Fast principal component extraction by a weighted information criterion. IEEE Transactions on Signal Processing, 2002, 50(8): 1994-2002 doi: 10.1109/TSP.2002.800395
[11]	Oja E, Ogawa H, Wangviwattana J. Principal component analysis by homogeneous neural networks, Part I: the weighted subspace criterion. IEICE Transactions on Information and Systems, 1992, E75-D(3): 366-375
[12]	Tanaka T. Generalized weighted rules for principal components tracking. IEEE Transactions on Signal Processing, 2005, 53(4): 1243-1253 doi: 10.1109/TSP.2005.843698
[13]	Bartelmaos S, Abed-Meraim K. Fast principal component extraction using Givens rotations. IEEE Signal Processing Letters, 2008, 15: 369-372 doi: 10.1109/LSP.2008.920006
[14]	Li J W, Li C X. Information criterion based fast PCA adaptive algorithm. Journal of Systems Engineering and Electronics, 2007, 18(2): 377-384 doi: 10.1016/S1004-4132(07)60101-7
[15]	Thameri M, Abed-Meraim K, Belouchrani A. Low complexity adaptive algorithms for principal and minor component analysis. Digital Signal Processing, 2013, 23(1): 19-29 doi: 10.1016/j.dsp.2012.09.007
[16]	Thameri M, Kammoun A, Abed-Meraim K, Belouchrani A. Fast principal component analysis and data whitening algorithms. In: Proceedings of the 7th International Workshop on Systems, Signal Processing and their Applications. Tipaza, Algeria: IEEE, 2011. 139-142
[17]	Chen T P, Amari S I, Lin Q. A unified algorithm for principal and minor components extraction. Neural Networks, 1998, 11(3): 385-390 doi: 10.1016/S0893-6080(98)00004-5
[18]	Kong X Y, An Q S, Ma H G, Han C Z, Zhang Q. Convergence analysis of deterministic discrete time system of a unified self-stabilizing algorithm for PCA and MCA. Neural Networks, 2012, 36: 64-72 doi: 10.1016/j.neunet.2012.08.016
[19]	Oja E. Principal components, minor components and linear neural networks. Neural Networks, 1992, 5(6): 927-935 doi: 10.1016/S0893-6080(05)80089-9
[20]	Kung S Y, Diamantaras K I, Taur J S. Adaptive principal component extraction (APEX) and applications. IEEE Transactions on Signal Processing, 1994, 42(5): 1202-1217 doi: 10.1109/78.295198
[21]	Möller R. A self-stabilizing learning rule for minor component analysis. International Journal of Neural Systems, 2004, 14(1): 1-8 doi: 10.1142/S0129065704001863
[22]	方蔚涛, 马鹏, 成正斌, 杨丹, 张小洪.二维投影非负矩阵分解算法及其在人脸识别中的应用.自动化学报, 2012, 38(9): 1503-1512 http://www.aas.net.cn/CN/abstract/abstract17761.shtml Fang Wei-Tao, Ma Peng, Cheng Zheng-Bin, Yang Dan, Zhang Xiao-Hong. 2-dimensional projective non-negative matrix factorization and its application to face recognition. Acta Automatica Sinica, 2012, 38(9): 1503-1512 http://www.aas.net.cn/CN/abstract/abstract17761.shtml