 
Summary: Focus Article
Centroid
Herv´e Abdi
The concept of centroid is the multivariate equivalent of the mean. Just like the
mean, the centroid of a cloud of points minimizes the sum of the squared distances
from the points of the cloud to a point in the space . 2009 John Wiley & Sons, Inc.
Centroid
The notion of centroid generalizes the notion of
a mean to multivariate analysis and multidimen
sional spaces. It applies to vectors instead of scalars,
and it is computed by associating to each vector a mass
which is a positive number taking values between 0
and 1 and such that the sum of all the masses is equal
to 1. The centroid of a set of vectors is also called the
center of gravity, the center of mass, or the barycenter
of this set.
NOTATIONS AND DEFINITION
Let V be a set of I vectors with each vector being
composed of J elements
V = {v1, . . . , vi, . . . , vI} with
