# Segment 29. GMMs in N-Dimensions

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## Contents

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

{{#widget:Iframe |url=http://www.youtube.com/v/PH8_qqDTCYY&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/PH8_qqDTCYY

Links to the slides: PDF file or PowerPoint file

### Problems

#### To Compute

The file twoexondata.txt contains data similar to that shown in slide 6, as 3000 (x,y) pairs.

1. In your favorite computer language, write a code for K-means clustering, and cluster the given data using (a) 3 components and (b) 8 components. Don't use anybody's K-means clustering package for this part: Code it yourself. Hint: Don't try to do it as limiting case of GMMs, just code it from the definition of K-means clustering, using an E-M iteration. Plot your results by coloring the data points according to which cluster they are in. How sensitive is your answer to the starting guesses?

2. In your favorite computer language, and either writing your own GMM program or using any code you can find elsewhere (e.g., Numerical Recipes for C++, or scikit-learn, which is installed on the class server, for Python), construct mixture models like those shown in slide 8 (for 3 components) and slide 9 (for 8 components). You should plot 2-sigma error ellipses for the individual components, as shown in those slides.

#### To Think About

1. The segment (or the previous one) mentioned that the log-likelihood can sometimes get stuck on plateaus, barely increasing, for long periods of time, and then can suddenly increase by a lot. What do you think is happening from iteration to iteration during these times on a plateau?