Abstract：By introducing the nonholonomic constraints, the nonholonomic natural gradient algorithm effectively overcomes the shortcoming and the insufficiency of the traditional natural gradient algorithm, namely,it can still work well when the amplitude of source signal changes rapidly over time or is equal to zero in a certain period of time. Meanwhile, the sign operator derived from a general dynamic separation model can improve the convergence of the algorithm. Thus, a nonholonomic natural gradient algorithm based on the sign operation is obtained by combining the above two ideas. Furthermore, a variable step-size based on the gradient of cost function is also applied to the proposed algorithm to balance the contradiction between the convergence speed and the steady-state error. The simulation results show that the performance of the proposed algorithm is superior to that of traditional algorithm, and it improves convergence speed without worsening the steady-state error seriously.
季策，杨坤，王艳茹，刘梦蝶. 基于符号算子的变步长不完整自然梯度算法*[J]. 模式识别与人工智能, 2014, 27(11): 1026-1031.
JI Ce, YANG Kun, WANG Yan-Ru, LIU Meng-Die. Variable Step-Size Nonholonomic Natural Gradient Algorithm Based on Sign Operator. , 2014, 27(11): 1026-1031.
[1] Sansrimahachai P, Ward D B, Constantinides A G. Blind Source Separation of Instantaneous MIMO Systems Based on the Least-squares Constant Modulus Algorithm. IEE Proceedings－Vision, Image Signal Process, 2005, 152(5): 616-622 [2] Zhang X S, Jiang J, Peng S L. Blind Super-Resolution Reconstruction Algorithm under Affine Motion Model. Pattern Recognition and Artificial Intelligence, 2012, 25(4): 648-655 (in Chinese) (张雪松,江 静,彭思龙.放射运动模型下的图像盲超分辨率重建算法.模式识别与人工智能, 2012, 25(4): 648-655) [3] Choi C H, Chang W, Lee S Y. Blind Source Separation of Speech and Music Signals Using Harmonic Frequency Dependent Indepen-dent Vector Analysis. Electronics Letters, 2012, 48(2): 124-125 [4] Hesse C W, James C J. On Semi-Blind Source Separation Using Spatial Constraints with Applications in EEG Analysis. IEEE Trans on Biomedical Engineering, 2006, 53(12): 2525 -2534 [5] Amari S I, Chen T P, Cichocki A. Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation. Neural Computation, 2000, 12(6): 1463-1484 [6] Niu Y L, Wang Y M, Wang Y. Improved Adaptive Algorithm of Blind Source Separation Based on Nonholonomic Natural Gradient. Pattern Recognition and Artificial Intelligence, 2006, 19(5): 667-673 (in Chinese) (牛奕龙,王英民,王 毅.一种改进的自适应不完整自然梯度盲源分离算法.模式识别与人工智能, 2006, 19(5): 667-673) [7] Li G B, Zhang J Y. Adaptive Step-Size Natural Gradient Algorithm Based on Separating Degree. Signal Processing, 2007, 23(3): 429-432 (in Chinese) (李广彪,张剑云.基于分离度的步长自适应自然梯度算法.信号处理, 2007, 23(3): 429-432) [8] Ji C, Tang B C, Zhu L C. Blind Source Separation of Speech Signals Based on Variable Step Length Natural Gradient Algorithm. Journal of Central South University: Science and Technology, 2011, 42(S1): 661-665 (in Chinese) (季 策,汤宝成,朱丽春.基于变步长自然梯度算法的语音信号盲分离.中南大学学报:自然科学版, 2011, 42(S1): 661-665) [9] Ji C, Yu P, Yu Y. Blind Source Separation Based on Improved Natural Gradient Algorithm // Proc of the 8th World Congress on Intelligent Control and Automation. Jinan, China, 2010: 6804-6807 [10] Zhang Z L, Yi Z. An Efficient Independent Component Analysis Algorithm for Sub-Gaussian Sources // Proc of the 2nd International Symposium on Neural Networks. Chongqing, China, 2005: 967-972 [11] Yuan L X, Wang W W, Chambers J A. Variable Step-Size Sign Natural Gradient Algorithm for Sequential Blind Source Separation. IEEE Signal Processing Letters, 2005, 12(8): 589-592 [12] Cichocki A, Amari S I. Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Chichester, UK: John Wiley & Sons, Inc., 2002 [13] Zhang Y L, Lou S T, Zhang W T, et al. Blind Source Separation Algorithm of Natural Gradient Based on Estimation of Score Function. Journal of Data Acquisition and Processing, 2011, 26(2): 167-171 (in Chinese) (张延良,楼顺天,张伟涛,等.基于分值函数估计的自然梯度盲分离算法.数据采集与处理, 2011, 26(2): 167-171)
2014, Vol. 27 
