Homework 9 Implement the EM algorithm




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Homework 9

In this homework, you are required to include in your report the code that you
implemented. If you use some code from the web or package, also mention in your
report the origin of the code.
1. Implement the EM algorithm for clustering with multivariate Gaussian models discussed in the LearningGM section. Initialize the algorithm with the K-means result
(for example Matlab provides a kmeans function). Assume there are only two clusters. Report the parameters πk, µk, Σk, k = 1, 2 for the following datasets containing
500-600 observations from R
a) The dataset xeasy. (1 point)
b) The dataset x1. (1 point)
c) The dataset x2. (2 points)
Pay attention to the dimensions of the mean centers µk, k = 1, 2 and the covariance
matrices Σk, k = 1, 2.
2. Now implement the two-step EM algorithm (also known as provable EM) and repeat
the questions from problem 1. (4 points)