Projection pursuit has been widely used for blind source separation, so it is very important in independent component analysis.
The first successful implementation is due to Jerome H. Friedman and John Tukey (1974), who named projection pursuit.
The most exciting feature of projection pursuit is that it is one of the very few multivariate methods able to bypass the "curse of dimensionality" caused by the fact that high-dimensional space is mostly empty.
This is a distinct advantage over methods based on interpoint distances like minimal spanning trees, multidimensional scaling and most clustering techniques.
Many of the methods of classical multivariate analysis turn out to be special cases of projection pursuit.