Investigation on the skewness for independent component analysis

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.