A NOTE ON FINDING EXTREME-POINTS IN MULTIVARIATE SPACE

Extreme points in multivariate space have many applications in statistics and can be studied as vertices of a convex polytope (hulls). Finding such vertices is a major topic of study in computational geometry but has received very little attention in applied statistics. Three new methods, based on random and restricted random sampling, is introduced for finding vertices of convex hulls of a sample of N points in k space. Simple projections are used iteratively to find the extreme points. Compared to existing methods, the new method utilizes raw computing power over theoretical analysis and is efficient for practical problems. © 1990.