# Clustering with probabilities

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

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I am not completely sure of your question, but it seems like you could be satisfied with some simple clustering algorithm like en.wikipedia.org/wiki/K-means_clustering –  utdiscant Mar 5 '12 at 13:11
I don't understand what you mean. Maybe it would help if you explained more what you mean by "observation." Also, what do you mean by closest? What's this for? The dude that answered above me is probably onto something, though. –  Taylor Mar 5 '12 at 16:13
+1 to @whuber for being a dude. :) –  Michelle Mar 5 '12 at 21:40
This sounds like latent class analysis - I suggest looking into that –  Macro Apr 5 '12 at 12:03
I will explain: we observe a system and we have a set of subjects that have done a given action. After observation we infer a set A with the probabilities relative to each subject having done the action. I want to cluster the set of subjects on subsets or clusters which groups subjects according to the prababilities. I want to cluster and measure the distance between clusters for evaluate the amount of information we have after observation. I am also interested in detecting outliers. –  Ben Apr 10 '12 at 11:14

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.

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(+1) or Kernel Density estimation as a more generic approach –  steffen Apr 5 '12 at 10:13

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'.

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but the number of clusters is not known –  Ben Apr 10 '12 at 11:07