偏度在独立元分析模型中的作用分析及算法设计

Investigation on the skewness for independent component analysis

相对于峭度(kurtosis),偏度(skewness)历来在独立元分析(ICA)的研究中就没有得到充分重视.尤其是当关于峭度符号的一比特匹配定理在理论上被证明了以后,偏度似乎更是变成了ICA模型中的一个无用统计量.但当信号的峭度很小或者其非Gauss性主要源自于偏度时,仅仅利用峭度信息是不足够的.本文目的就在于分析和讨论在此种情况下独立元分析如何利用偏度信息.首先从理论上分析了偏度在ICA模型中的作用,结果表明在偏度上并不存在与峭度类似的一比特匹配定理,也就是说,算法中模型密度函数的选择无需考虑其偏度与源信号偏度的符号匹配问题.在此基础上,本文进一步提出了一套灵活的模型密度函数设计方法,并提出了一个算法实例,它可以适用于具有任意偏度和峭度组合的信号.

Skewness has received much less attention than kurtosis in the independent component analysis （ICA）.In particular,the skewness seems to become a useless statistics after the kurtosis related one-bit-matching theorem was proven.However,as the non-Gaussianity of one signal comes mainly from skewness,it is intuitively understandable that its recovery should not rely on kurtosis.In this paper we discuss the skewness based ICA,and show that any probability density function （pdf） with non-zero skewness can be employed by ICA for the recovery of the source with non-zero skewness,without needing to consider the skewness sign.The observation together with the one-bit-matching theorem provides a basic guideline for the model pdf design in ICA algorithm.