I am looking for a measure of the amount of spread or variance of a number of points which would work for different numbers of clusters. I am looking for something fast to compute and not necessarily computing the number of clusters or the positions of the centroids. Ideally an algebraic function.
In practice, I need this measure to be zero if all the points are equal, and maximum when all the points are equidistants. Situations with points clustering around 1,2,3 clusters would get increasing values and situations where the points are more loosely clustered would get higher values.
I have tried different things based on pairwise distances, but I can't find the right combination. I am quite sure it exists. I kind of want the average intra-cluster distance without knowing the number of clusters...
- dimensionality is low as I always have vectors of scalars
- I have few points at a time (a hundred at most)
- it really needs to be fast, I have no time for k-means and elbow method.
Thanks a lot for your help and sorry if my explanation is not clear.