一种广义主成分提取算法及其收敛性分析

高迎彬; 孔祥玉; 胡昌华; 张会会; 侯立安

doi:10.11999/JEIT151433

一种广义主成分提取算法及其收敛性分析

doi: 10.11999/JEIT151433

基金项目:

国家自然科学基金面上项目(61074072, 61374120)，国家杰出青年基金(61025014)

计量
- 文章访问数: 1481
- HTML全文浏览量: 132
- PDF下载量: 335
- 被引次数: 0
出版历程
- 收稿日期: 2015-12-17
- 修回日期: 2016-05-10
- 刊出日期: 2016-10-19

A Generalized Principal Component Extraction Algorithm and Its Convergence Analysis

Funds:

The National Natural Science Foundation of China (61074072, 61374120), The National Science Fund for Distinguished Youth Scholars (61025014)

摘要

摘要: 广义主成分分析在现代信号处理的诸多领域发挥着重要的作用。目前，自适应广义主成分分析算法还并不多见。针对这一现状，该文提出一种快速收敛的广义主成分分析算法，并通过理论分析所提算法的确定性离散时间系统，导出了保证算法收敛的学习因子和初始权向量模值等边界条件。仿真实验和实际应用验证了所提算法的正确性和有用性。仿真结果还表明，所提算法比现有同类算法具有更快的收敛速度和更高的估计精度。
- 广义主成分 /
- 确定性离散时间 /
- 收敛性分析 /
- 神经网络
Abstract: The generalized principal component analysis plays an important roles in many fields of modern signal processing. However, up to now, there are few algorithms, which can extract the generalized principal component adaptively. In this paper, a generalized principal component extraction algorithm, which has fast convergence speed, is proposed. The corresponding Deterministic Discrete Time (DDT) system of the proposed algorithm is analyzed and some conditions about the learning rate and initial weight vector are also obtained. Finally, computer simulation and practical application results show that compared with some existing algorithms, the proposed algorithm has faster convergence speed and higher estimation accuracy.
- Generalized principal component /
- Deterministic Discrete Time (DDT) /
- Convergence analysis /
- Neural networks

HTML全文

参考文献(15)

谢荣, 刘峥, 刘俊. 基于矩阵束的MIMO雷达低仰角快速估计方法[J]. 电子与信息学报, 2011, 33(8): 1833-1838. doi: 10.3724/SP.J.1146.2010.01242.

XIE Rong, LIU Zheng, and LIU Jun. Fast algorithm for low elevation estimation based on matrix pencil in MIMO radar[J]. Journal of Electronics Information Technology, 2011, 33(8): 1833-1838. doi: 10.3724/SP.J.1146.2010.01242.

蔡振浩, 赵昆, 陈文. TD-LTE-A 系统下行多用户CoMP 联合预编码算法[J]. 北京邮电大学学报, 2015, 38(1): 67-70.

CAI Zhenhao, ZHAO Kun, and CHEN Wen. Research on CoMP joint transmission for downlink MU-MIMO in TD-LTE-A[J]. Journal of Beijing University of Posts and Telecommunications, 2015, 38(1): 67-70.

ANA Maria Tom. The generalized eigen-decomposition approach to the blind source separation problem[J]. Digital Signal Processing, 2006, 16: 288-302.

ZHANG Weitao, LOU Shuntian, and FENG Dazheng. Adaptive quasi-newton algorithm for source extraction via CCA approach[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(4): 677-689.

WANG Shougen and ZHAO Shuqin. An algorithm for Ax = Bx with symmetric and positive-definite A and B[J]. SIAM Journal on Matrix Analysis and Applications, 1991, 12(4): 654-660.

YANG Jian, XI Hongsheng, and YANG Feng. RLS-based adaptive algorithms for generalized eigen-decomposition[J]. IEEE Transactions on Signal Processing, 2006, 54(4): 1177-1188.

YANG Jian, HU Han, and XI Hongsheng. Weighted non-linear criterion-based adaptive generalised eigen decomposition[J]. IET Signal Processing, 2013, 7(4): 285-295.

Tuan Duong Nguyen and Isao Yamada. 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.

MLLER R. A self-stabilizing learning rule for minor component analysis[J]. International Journal of Neural Systems, 2004, 14(1): 1-8.

ZUFIRIA P J. On the discrete-time dynamics of the basic Hebbian neural-network node[J]. IEEE Transactions on Neural Networks, 2002, 13(6): 1342-1352.

GAO Yingbin, KONG Xiangyu, HU Changhua, et al. Convergence analysis of mller algorithm for estimating minor component[J]. Neural Processing Letters, 2015, 42(2): 355-368.

Tuan Duong Nguyen and IsaoYamada. Necessary and sufficient conditions for convergence of the DDT systems of the normalized PAST algorithms[J]. Signal Processing, 2014, 94: 288-299.

ATTALLAH S and ABED-MERAIM K. A fast adaptive algorithm for the generalized symmetric eigenvalue problem[J]. IEEE Signal Processing Letters, 2008, 15: 797-800.

施引文献

资源附件(0)

访问统计