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.

  • $\begingroup$ Can you describe your data, both the concepts behind what is being measured, and also the kinds of variables? $\endgroup$ – Alexis May 9 '14 at 15:03
  • $\begingroup$ Knowing euclidean distances between points automatically means knowing the multivariate variance in these data. Does variance look right to you as a measure of diversity? $\endgroup$ – ttnphns May 10 '14 at 5:20
  • $\begingroup$ Is it something in that line azimuth.mathforge.org/discussion/1311/… ? $\endgroup$ – Piotr Migdal Jul 24 '14 at 13:56

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