Sorry for the late reply, real life is trying to catch me ;)

On Wednesday 02 April 2008, Ankur (JIRA) wrote:
>     [
> https://issues.apache.org/jira/browse/MAHOUT-4?page=com.atlassian.jira.plug
>in.system.issuetabpanels:comment-tabpanel&focusedCommentId=12584544#action_1
>2584544 ]
>
> Ankur commented on MAHOUT-4:
> ----------------------------
> So here is a short write-up in my words, please feel free to
> fill any gaps/errors found

I will try to do so from my perspective, maybe others can add their views.


> Expectation Maximization for clustering
> -----------------------------------------------------
>  Let
>      z = unobserved data, clusters in our case.
>      y = observed data, points in our case.
>
>  p(y1|z1) + p(y2|z1) + p(y3|z1) + p(y4|z1) = 1
>  p(z1) + p(z2) = 1

Looks correct to me.


>  E-Step.
>  ------
>  M-Step
>  ------

I could not find an error in neither of the two steps so far.


> Questions
> =========
> 1. When and how do we re-compute the cluster centers ?

EM does not work with explicit cluster centers. In kmeans you iterate two 
steps: Assigning points to centers and recomputing the centers. In EM you 
again iterate two steps: Computing the probabilities for each point belonging 
to the clusters (so you do not assign them hard to one cluster, you only say 
with probability P it belongs to clusters i to k), in the second step you 
recompute the parameters of each cluster - the cluster center is influenced 
by each point but only weighted by its probability of belonging to this 
cluster.
 

> 2. As per my understanding points and clusters are simply labels with some
>    conditional probability assigned to them. A distance metric like one
>    used in K-means is nowhere involved, is that correct ?

Yes and no: Technically no, conceptually, your computation for the probability 
of assigning a point to a cluster should be based on the point's distance to 
the cluster.

I hope I did not cause more confusion than helping you. Maybe others can 
correct me or clarify what I left unclear...

Isabel


-- 
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