Clustering with probabilities

Question

I will ask my question beginning by an example (I am novice in stats) I have a set of probabilities from a given observation A={0.3,0.2,0.001, 0.02, ...} I want to partition A on subsets or clusters so as each one will contain the closest probabilities. And after, i will be interested in calculating the distances between the clusters. Is there any simple algorithm I can use for this?

Thanks

Answer 1

If A is an one-dimensional data set like the one you mentioned, I think a simple histogram will give the simple of clustering and distance.

Answer 2

There are several algorithms to do this.

The simplest is k-means, one implementation of which is:

• you pick the number of clusters you want, K
• you choose the centre of the clusters randomly to start with. There are K clusters, so K cluster centers
• now you iterate:
  • first you look at each point, and assign it to the nearest cluster centre
  • then, once you've assigned all the points to the clusters, you take the average of all the points in each cluster, and that becomes the new cluster centre, of that cluster

A good resource for learning clustering is 'Pattern Recognition and Machine Learning', by Christopher M. Bishop, chapter 9 'Mixture models and EM'.