[Solved] 685-621 Homework4

1. Problem 1
   • Points Total

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 _k,_k,p_k.

3. Problem 3
   • Points Total 15 Points Each

Consider three mean values of = [₁,₂,₃] = [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 _k,_k,p_k.