Tianping Chen Hong Chen Blind Extraction of Stochastic

发现和创新 算法及其稳定性分析 • 在下述文章中， • Tianping Chen Hong Chen, "Blind Extraction of Stochastic and Deterministic Signals by Neural Network Approach, “ 28 th Asilomar Conference on Signals, Systems and Computers” Edited by Avtar Singh，IEEE Computer Society Press (1994) p. 892 -896

不可积盲信号分离算法 • 在文章 • Shun-ichi Amari, Tianping Chen and Andrzej Cichocki. "Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation" Neural Computation Vol. 12, (2000) pp. 1463 -148

A=[ 1. 00000001 0. 99999998 0. 9999 1. 00000001 1. 00000002 1. 00000001 1. 0000] 混合矩阵严重病态

• IEEE Transactions on Signal Processing, 11(6), 1490 -1497, 2000 • Interestingly, (12) belongs to a family of Blind source separation procedure in which a nonholonomic constrain is imposed on W(t) ([13]) • 有意思的是, 算法(12) 属于一类带不可积 (nonholonomic) 约束的盲信号分离算法. • ([13]) 即我们的文章 • 其它引用文章就不再列出

在多本专著中被引用 • Independent Component Analysis, A Volume in the Wiley Series on Adaptive Learning on Signal Processing • Advances in Independent Component Analysis, Springer 2000 • Unsupervised Adaptive Filtering, Vol. 1, A Volume in the Wiley Series on Adaptive Learning on Signal Processing… • Unsupervised Adaptive Filtering, Vol. 2, A Volume in the Wiley Series on Adaptive Learning on Signal Processing

This paper proposed a new learning algorithm, which works so well under fluctuating or temporally changing environments with a number of receiving signals being more than the number of source signals. Professor Chen first showed us by computer simulations how well the nonholonomic idea worked and gave the stability analysis. Then we collaborated for providing necessary mathematical foundation. • This paper gives a rigorous mathematical analysis of the stability of the information-based gradient learning algorithm. The idea was closed related to Professor Chen’s previous paper (1994), in which the stability analysis for feedforward neural network approach was first given in detail in the case of two signals. • In this paper, Professor Chen’s contribution is remarkable in the part of mathematical analysis….

Principal and minor components analyses are closely related problems, but their properties look quite different. We have unified the two in this paper for the first time. The idea was proposed by Professor Chen, and we collaborated for details of the mathematical proofs including the global stability analysis. This is continuation of the previous paper, and we gave more efficient and beautiful new algorithms. The idea was first proposed by Professor Chen and we collaborated for proving details.