Oja depth and centers of gravity

Pat Morin

The Oja depth of a point x with respect to a finite point set S, both in R^d, is the expected volume of a simplex whose vertices are x and d points chosen at random, without replacement, from S. In this talk, we present two results that relate the point of minimum Oja depth to the center of gravity of S and the center of gravity of the convex hull of S.

This is joint work with Dan Chen.