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 -- There is no sin but ignorance. -- Christopher Marlowe |\ _,,,---,,_ Web: <http://www.isabel-drost.de> /,`.-'`' -. ;-;;,_ |,4- ) )-,_..;\ ( `'-' '---''(_/--' `-'\_) (fL) IM: <xmpp://[EMAIL PROTECTED]>
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