Projection Pursuit the Two Basic Elements of Projection Pursuit Are: a Pp Index and a Pp Algorithm. A

Many data sets are high dimensional. It has been a common practice to use lower dimensional linear projections of the data for visual inspection. The lower dimension is usually 1 or 2 (or maybe 3). More precisely, if X 1 ; : : :; X n 2 IR p are p-dimensional data, then a k (< p)-dimensional linear projection is Z 1 ; : : : ; Z n 2 IR k where Z i = T X i for some p k matrix such that T = I k , the k-dimensional identity matrix. Such a matrix is often called orthonormal. When k = 1, may be called a direction and the structure of the projected data can be viewed through a histogram; when k = 2, the structure can be inspected through its scatter plot; and when k = 3, it can be comprehended by spinning a three-dimensional scatter plot. Since there are innnitely many projections from a higher dimension to a lower dimension, it is important to have a technique of pursuing a nite sequence of projections that can reveal the most interesting structures of the data. The idea of combining both projection and pursuit originates from Kruskal 18] and Switzer 26]. However, the rst successful implementation of the idea was by Friedman and Tukey 10], who also suggested the felicitous name Projection Pursuit (PP). A uniied mathematical notion of PP was introduced by Huber 14] which provided the basis for further statistical research in the area. More recent papers include