基于负熵准则盲分离方法的剖析与研究

Study of Approach of Blind Source Separation Based on Negentropy

从统计学原理、负熵近似计算、算法的稳定性定理、最大负熵方法的历史演变几个方面,对Hyvrinen负熵准则盲分离算法作出全面的剖析,指出:(1)在负熵ICA算法中,不应引用联合负熵的定义,只宜采用边缘负熵的定义;(2)中心极限定理只能为负熵ICA算法提供一定的直观解释,但不能成为算法的统计学依据;(3)Hyvrinen等人给出的负熵计算公式并不能正确度量随机变量的非高斯性;(4)负熵ICA算法实现盲分离的真正机理是信号非线性变换后均值的极值特性,由此极值特性提出负熵准则未必是合适的。

From the aspects of statistic principles, approximation of negentropy, stability theorem and historical clues, Hyvarinen＇s negentropy-based approach of blind source separation was analyzed in detail. The arguments were proposed： （1） In this approach of ICA, a definition of marginal negentropy, instead of joint negentropy should be stated. （2） The negentropy-based ICA could be partly interpreted by the Central Limit Theorem （CLT）. However, CLT could not be a convincing statistics base for the approach. （3） The formula of negentropy approximation presented by Hyvairinen can not correctly measure the non-gaussianity. （4） The actual mechanism of separating sources of the approach is the extremum property of expectation of a variable after non-linear transform. However, it may not be appropriate to derive from the criterion of negentropy.