 
Summary: Centroïd
Center of Gravity
Center of Mass
Barycenter)
Hervé Abdi1
1 overview
The notion of centroïd generalizes the notion of a mean to multi
variate analysis and multidimensional 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 centroïd
of a set of vectors is also called the center of gravity, the center of
mass, or the barycenter of this set.
2 Notations and definition
Let V be a set of I vectors with each vector being composed of J
elements
V = {v1,...,vi ,...,vI } with vi = vi,1,...,vi,j ,...,vi,J
T
. (1)
1
