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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.
In contrast to kurtosis, skewness has traditionally been overlooked in the study of independent element analysis (ICA), especially when the one-bit matching theorem for kurtosis is theoretically proven, Skewness seems to be more of a useless statistic in the ICA model, but it is not sufficient to use kurtosis information only when the kurtosis of the signal is small or its non-Gauss nature is mainly derived from skewness. It is to analyze and discuss how the independent meta-analysis makes use of the skewness information in this case.Firstly, the role of skewness in the ICA model is analyzed theoretically, and the result shows that there is no single bit similar to kurtosis in skewness Matching theorem, that is to say, the choice of model density function in the algorithm does not need to consider the problem of symbol matching between the skewness and the skewness of the source signal.On the basis of this, we propose a flexible design method of model density function An example of an algorithm, it can be applied to signals with any combination of skewness and kurtosis.