In exploratory projection pursuit [Friedman, 1987, Friedman and Tukey, 1974] the data is projected linearly, but this time a projection which reveals as much of the non-normally distributed structure of the data set as possible is sought. This is done by assigning a numerical ``interestingness'' index to each possible projection, and by maximizing the index. The definition of interestingness is based on how much the projected data deviates from normally distributed data in the main body of its distribution. There is also a neural implementation of this idea [Fyfe and Baddeley, 1995].
After an interesting projection has been found, the structure that makes the projection interesting may be removed from the data, after which the procedure can be restarted from the beginning to reveal more of the structure of the data set.