ps6 (1)

# ps6 (1) - Problem Set 6 MAS 622J/1.126J: Pattern...

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Problem Set 6 MAS 622J/1.126J: Pattern Recognition and Analysis Due Monday, 20 November 2006 [Note: All instructions to plot data or write a program should be carried out us- ing either Python accompanied by the matplotlib package or Matlab. Feel free to use either or both, but in order to maintain a reasonable level of consistency and simplicity we ask that you do not use other software tools.] Problem 1: Mixture of Gaussians Implement the EM algorithm for estimating the parameters of a mixture of Gaussians with isotropic covariances Σ j = σ j I . Note: The data sets are two± dimensional. To solve this problem you can write your own code or use any MATLAB/Python toolboxes available for the purpose. In particular there is a MATLAB mixture of Gaussians algorithm available for download here that would be good to explore: http://dataclustering.cse.msu.edu/ Experiment with the number of mixtures and comment on the tradeoﬀ between the number of mixtures and goodness of ²t (i.e. loglikelihood) of the data. Suggestion: Plot the loglikelihood as a function of the number of components of a mixture of Gaussians to support your argument. Find a ²xed number of Gaussians that works well for each data set. Plot the estimated Gaussians as one±sigma countours of each mixing com- ponent on top of the training data. List mean, covariance and mixing weights of each mixture component. Include

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## This note was uploaded on 12/04/2011 for the course ESD 1.124 taught by Professor Kevinamaratunga during the Fall '00 term at MIT.

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ps6 (1) - Problem Set 6 MAS 622J/1.126J: Pattern...

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