基于Hebbian规则的新型自适应广义主元分析算法

doi:10.11959/j.issn.1000-436x.2020134

通信学报 ›› 2020, Vol. 41 ›› Issue (7): 103-109.doi: 10.11959/j.issn.1000-436x.2020134

基于Hebbian规则的新型自适应广义主元分析算法

高迎彬^1,²,孔祥玉²,崔巧花¹,董海迪³

¹ 中国电子科技集团公司第五十四研究所，河北石家庄 050081
² 火箭军工程大学导弹工程学院，陕西西安 710025
³ 海军工程大学兵器工程学院，湖北武汉 430033

修回日期:2020-05-27 出版日期:2020-07-25 发布日期:2020-08-01
作者简介:高迎彬（1986- ），男，河北安平人，博士，中国电子科技集团公司第五十四研究所工程师，主要研究方向为自适应信号处理和阵列信号处理等|孔祥玉（1967- ），男，山西临汾人，博士，火箭军工程大学教授、博士生导师，主要研究方向为自适应信号处理、故障诊断和特征提取等|崔巧花（1987- ），女，河北邱县人，中国电子科技集团公司第五十四研究所工程师，主要研究方向为散射通信等|董海迪（1989- ），男，湖北武汉人，博士，海军工程大学讲师，主要研究方向为自适应信号处理和故障诊断等
基金资助:
国家自然科学基金资助项目(61833016);国家自然科学基金资助项目(61673387);国家自然科学基金资助项目(61374120);陕西省自然科学基金资助项目(2020JM-356)

Novel adaptive generalized principal component analysis algorithm based on Hebbian rule

Yingbin GAO^1,²,Xiangyu KONG²,Qiaohua CUI¹,Haidi DONG³

¹ The 54th Research Institute of China Electronics Technology Group Corporation,Shijiazhuang 050081,China
² College of Missile Engineering,Rocket Force University of Engineering,Xi’an 710025,China
³ College of Weaponry Engineering,Naval University of Engineering,Wuhan 430033,China

Revised:2020-05-27 Online:2020-07-25 Published:2020-08-01
Supported by:
The National Natural Science Foundation of China(61833016);The National Natural Science Foundation of China(61673387);The National Natural Science Foundation of China(61374120);The Natural Science Foundation of Shaanxi Province(2020JM-356)

摘要/Abstract

摘要：

为了从输入信号中自适应地对信号的广义主元进行估计，基于Hebbian线性神经元模型，提出了一种新型广义主元分析算法。该算法通过当前时刻的采样值来估计信号的自相关矩阵，有效地降低了算法的计算复杂度。利用 Lyapunov 稳定性定理进行平衡点分析表明：当且仅当神经元权向量收敛到信号的广义主元时，算法到达稳定状态。仿真实验表明：相比一些同类型算法，所提算法具有较快的收敛速度。

关键词: Hebbian规则, 广义主元, 平衡点, 自适应估计

Abstract:

In order to adaptively estimate the generalized principal component from input signals,a novel generalized principal component analysis algorithm was proposed based on the Hebbian linear neuron model.Since the autocorrelation matrices of the signals were estimated directly from the sampled data at the current time,the proposed algorithm had low computation complexity.Trough analyzing all of the equilibrium points by Lyapunov method,it is proven that if and only if the weight vector in the neuron had the same direction with the generalized principal component,the proposed algorithm attains the convergence status.Simulation results shows that compared with some same type algorithms,the proposed algorithm has faster convergence speed.

Key words: Hebbian rule, generalized principal component, equilibrium point, adaptive estimation

中图分类号:

TP391

高迎彬,孔祥玉,崔巧花,董海迪. 基于Hebbian规则的新型自适应广义主元分析算法[J]. 通信学报, 2020, 41(7): 103-109.

Yingbin GAO,Xiangyu KONG,Qiaohua CUI,Haidi DONG. Novel adaptive generalized principal component analysis algorithm based on Hebbian rule[J]. Journal on Communications, 2020, 41(7): 103-109.

图/表 4

参考文献 22

[1]	孔祥玉, 冯晓伟, 胡昌华 . 广义主成分分析算法及应用[M]. 北京: 国防工业出版社, 2018.
	KONG X Y , FENG X W , HU C H . General principal component analysis and its application[M]. Beijing: National Defense Industry PressPress, 2018.
[2]	董海迪, 刘刚, 何兵 ,等. 多维广义次成分提取准则及自适应算法[J]. 控制与决策, 2019,34(1): 105-112.
	DONG H D , LIU G , HE B ,et al. Mutiple minor generalized eigenvectors extraction information and its adaptive algorithm[J]. Control and Decision, 2019,34(1): 105-112.
[3]	YANG J , HU H , XI H . Weighted non-linear criterion-based adaptive generalised eigendecomposition[J]. IET Signal Processing, 2013,7(4): 285-295.
[4]	WANG R , GAO F , YAO M ,et al. Adaptive algorithms for generalized eigenvalue decomposition with a nonquadratic criterion[J]. Chinese Journal of Electronics, 2013,22(4): 807-813.
[5]	GAO Y B , KONG X , ZHANG Z ,et al. An adaptive self-stabilizing algorithm for minor generalized eigenvector extraction and its convergence analysis[J]. IEEE Transactions on Neural Networks ＆Learning Systems, 2018,29(10): 4869-4881.
[6]	庄陵, 马靖怡, 王光宇 ,等. FIR数字滤波器零极点灵敏度分析及优化实现[J]. 通信学报, 2018,39(9): 168-177.
	ZHUANG L , MA J Y , WANG G Y ,et al. Analysis and optimal realization of pole-zero sensitivity for FIR digital filters[J]. Journal on Communications, 2018,39(9): 168-177.
[7]	MATHEW G , REDDY V U , DASGUPTA S . Adaptive estimation of eigensubspace[J]. IEEE Transactions on Signal Processing, 1994,43(2): 401-411.
[8]	HEBBIAN D . The organization of behavior[M]. New Jersey: John Wiley ＆ SonsPress, 1949.
[9]	OJA E . A simplified neuron model as a principal component analyzer[J]. Journal of Mathematical Biology, 1982(15): 267-273.
[10]	FENG X , KONG X , DUAN Z ,et al. Adaptive generalized eigen-pairs extraction algorithms and their convergence analysis[J]. IEEE Transactions on Signal Processing, 2016,64(11): 2976-2989.
[11]	CHATTERJEE C , ROYCHOWDHURY V , RAMOS J ,et al. Self-organizing algorithms for generalized eigen-decomposition[J]. IEEE Transactions on Neural Networks, 1997,8(6): 1518-1530.
[12]	LIU L , SHAO H , NAN D . Recurrent neural network model for computing largest and smallest generalized eigenvalue[J]. Neurocomputing, 2008,71: 3589-3594.
[13]	TANAKA T . Fast generalized eigenvector tracking based on the power method[J]. IEEE Signal Processing Letters, 2009,16(11): 969-972.
[14]	NGUYEN T , TAKAHASHI N , YAMADA I . An adaptive extraction of generalized eigensubspace by using exact nested orthogonal complement structure[J]. Multidimensional Systems and Signal Processing, 2013,24(3): 457-483.
[15]	LI H , DU B , KONG X ,et al. A generalized minor component extraction algorithm and its analysis[J]. IEEE Access, 2018(6): 36771-36779.
[16]	M?LLER R . Derivation of coupled PCA and SVD learning rules from a Newton zero-finding framework[R]. Berlin:Computer Engineering,Faculty of Technology,Bielefeld University, 2017.
[17]	NGUYEN T D , YAMADA I . Adaptive normalized quasi-Newton algorithms for extraction of generalized eigen-pairs and their convergence analysis[J]. IEEE Transactions on Signal Processing, 2013,61(6): 1404-1418.
[18]	KAKIMOTO K , YAMAGISHI M , YAMADA I . Acceleration of adaptive normalized quasi-Newton algorithm with improved upper bounds of the condition number[C]// 2017 IEEE International Conference on Acoustics,Speech and Signal Processing. Piscataway:IEEE Press, 2017: 4267-4271.
[19]	UCHIDA K , YAMADA I . A nested ?1-penalized adaptive normalized quasi-newton algorithm for sparsity-aware generalized eigen-subspace extraction[C]// 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference.[S.n.:s.l. ], 2018: 212-217.
[20]	UCHIDA K , YAMADA I . An ?1-penalization of adaptive normalized quasi-Newton algorithm for sparsity-aware generalized eigenvector estimation[C]// 2018 IEEE International Conference on Statistical Signal Processing Workshop. Piscataway:IEEE Press, 2018: 528-532.
[21]	FARHANG B . Adaptive filters:theory and applications[M]. 2nd ed. New Jersey: John Wiley ＆ SonsPress, 2013.
[22]	ZHANG L . On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere[J]. Computational Optimization and Applications, 2013,54(1): 111-139.

基于Hebbian规则的新型自适应广义主元分析算法

Novel adaptive generalized principal component analysis algorithm based on Hebbian rule

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 4

参考文献 22

相关文章 1

Metrics

推荐阅读 0