I wish to measure the "diversity" of a group of objects. Right now I'm using Euclidean distance to compute the similarity matrix between all the objects in the group.
I'm searching for a measure of this diversity to decide if replacing an element of this matrix with a new one will make the group more or less homogeneous. I wish to end up the most heterogeneous group.
Of course, I'm open to another approaches if I'm looking at this from the wrong angle.
Bonus points if it's computationally efficient.