1. Problem 1 In this problem, develop pseudocode and code for the Expectation Maximization method. This should be done for a generic number of clusters, at a minimum you should be able to handle 3 clusters to build a three class classifiers. Using the following data
x (1)
for 5 iteration show the values for +1) using your code. You can either use a built in EM algorithm or the one you implement to show how well the clusters create the two separations as in slide 15 of the Expectation Maximization.pdf for the 5 iterations. In this example, are the clusters starting to converge? If no, why not? If yes, why?
2. Problem 2 Using the EM algorithm from Problem 1 the IRIS data set estimate the the unknown parameters µk,σk,pk.
3. Problem 3
Consider three mean values of µ = [µ1,µ2,µ3] = [4.5,2.2,3.3] with a corresponding covariance matrix as follows:
(2)
The respective minimums are min = [3.5,1.7,2.5] and maximums are max = [5.5,2.7,4.1].
Generate 300 observations.
Using the EM algorithm from Problem 1 and the generated date estimate the the unknown parameters µk,σk,pk.
