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Unformatted text preview: Computational functional genomics (Spring 2005: Lecture 8) David K. Gifford (Adapted from a lecture by Tommi S. Jaakkola) MIT CSAIL Topics • Basic clustering methods – hierarchical – kmeans – mixture models • Multivariate gaussians • Principle Component Analysis Simple mixture models • Instead of representing clusters only in terms of their centroids, we can assume that each cluster corresponds to some distribution of examples such as Gaussian Two clusters, two Gaussian models N ( µ 1 , σ 2 ), N ( µ 2 , σ 2 ) • • The partial assignment of examples to clusters should be based on the probabilities that the models assign to the examples Simple mixture model clustering (for cluster models with fixed covariance) • The procedure: 1. Pick k arbitrary centroids 2. Assign examples to clusters based on the relative likelihoods that the cluster models assign to the examples 3. Adjust the centroids to the weighted means of the examples 4. Goto step 2 (until little change) Simple mixture models • We can also adjust the covariance matrices in the Gaussian cluster models Ideas how? • • In this case the clusters can become more elongated Simple mixture models • A generative model perspective: We are fitting a generative model to the observed data via the maximum likelihood principle Simple mixture models • A generative model perspective: We are fitting a generative model to the observed data via the maximum likelihood principle X ∼ N ( µ 1 , Σ 1 ) X ∼ N ( µ k , Σ k ) Statistical...
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.
 Spring '08
 BobSauer
 Genomics

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