Projection Persuit into three dimensional space

In this paper we discuss projection pursuit into three dimensions. In the previous works, practically one- and two-dimensional projection pursuit have been dealt to find interesting structures of data. We identify structures of data with three-dimensional projection pursuit, which can not find with lower dimensional projection pursuit. The Friedman index is chosen as a projection index to extend to three dimensions, and compared with the moments index, which han been proposed by Nason in 1995. We also demonstrate the effectiveness of the method with some numerical examples. The examples show the three-dimensional projection pursuit can reveal three-dimensional structures in high dimensional data space that is difficult to find out with two-dimensional projection pursuit.