Methodology and Statistics
International Conference, 17  19 September 2001
FDV, Ljubljana, Slovenia
A view of some centrality and consensus functions
in classification theory and beyond
Fred R. McMorris
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL 60616
USA
The notions of centrality and distancebased consensus are important
concerns in many areas such as social network theory and classification
theory. The general setup consists of a finite metric space X and a subset
S of X. For x in X, let D(x,S) be a measure of 'remoteness' of x to S, and
let L be the function where L(S) is the set of all points x in X for which
D(x,S) is minimum. L is called the median function on X when D(x,S) is the
sum of distances of x to all the points in S, L is called the mean function
on X when D(x,S) is the sum of the squared distances, and L is called the
center function on X when D(x,S) is the maximum of the distances of x to
all the points in S. This talk will review recent results obtained toward
characterizing the median, mean and center functions on metric spaces such
as certain classes of graphs (symmetric networks) and spaces of various
types of classifications on a fixed set of entities.
