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.
高迎彬,孔祥玉,胡昌华,张会会,侯立安. 一种广义主成分提取算法及其收敛性分析[J]. 电子与信息学报, 2016, 38(10): 2531-2537.
GAO Yingbin, KONG Xiangyu, HU Changhua, ZHANG Huihui, HOU Li’an. A Generalized Principal Component Extraction Algorithm and Its Convergence Analysis. JEIT, 2016, 38(10): 2531-2537.
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.
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.
[3]
ANA Maria Tomé. The generalized eigen-decomposition approach to the blind source separation problem[J]. Digital Signal Processing, 2006, 16: 288-302.
[4]
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.
[5]
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.
[6]
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.
[7]
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.
[8]
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.
[9]
MÖLLER R. A self-stabilizing learning rule for minor component analysis[J]. International Journal of Neural Systems, 2004, 14(1): 1-8.
[10]
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.
[11]
GAO Yingbin, KONG Xiangyu, HU Changhua, et al. Convergence analysis of möller algorithm for estimating minor component[J]. Neural Processing Letters, 2015, 42(2): 355-368.
[12]
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.
[13]
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.