Machine Learning Lecture 9: Clustering. Moshe Koppel Slides adapted from Raymond J. Mooney. Clustering. Partition unlabeled examples into disjoint subsets of clusters , such that: Examples within a cluster are very similar Examples in different clusters are very different
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Hierarchical ClusteringStart with all instances in their own cluster.
Until there is only one cluster:
Among the current clusters, determine the two
clusters, ci and cj, that are most similar.
Replace ci and cj with a single cluster ci cj
Let d be the distance measure between instances.
Select k random instances {s1, s2,… sk} as seeds.
Until clustering converges or other stopping criterion:
For each instance xi:
Assign xi to the cluster cjsuch that d(xi, sj) is minimal.
(Update the seeds to the centroid of each cluster)
For each cluster cj
sj = (cj)
Reassign clusters
Compute centroids
Reasssign clusters
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Compute centroids
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K Means Example(K=2)Reassign clusters
Converged!
Each step decreases objective function:
is minimized when µ is centroid of X.
Prob.
Classifier
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EMM step:
Retrain classifier on relabeled data
Continue EM iterations until probabilistic labels on unlabeled data converge.
Randomly assign examples probabilistic category labels.
Use standard naïveBayes training to learn a probabilistic model
with parameters from the labeled data.
Until convergence or until maximum number of iterations reached:
EStep: Use the naïve Bayes model to compute P(ci  E) for
each category and example, and relabel each example
using these probability values as soft category labels.
MStep: Use standard naïveBayes training to reestimate the
parameters using these new probabilistic category labels.
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Prob. Learner
Prob.
Classifier
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SemiSupervised EMContinue retraining iterations until probabilistic labels on unlabeled data converge.