ICA by Maximization of Nongaussianity
Aapo Hyvärinen, Juha Karhunen, Erkki Oja · 2001
In this chapter, the authors introduce a simple and intuitive principle for estimating the model of independent component analysis (ICA). This is based on maximization of nongaussianity. The authors start by intuitively motivating the maximization of nongaussianity by the central limit theorem. As a first practical measure of nongaussianity, they introduce the fourth-order cumulant, or kurtosis. Using kurtosis, they derive practical algorithms by gradient and fixed-point methods. Next, to solve some problems associated with kurtosis, the authors introduce the information-theoretic quantity called negentropy as an alternative measure of nongaussianity, and derive the corresponding algorithms for this measure. Finally, they discuss the connection between these methods and the technique called projection pursuit.