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Homework #6
Data Science I
1. In this problem, you will generate simulated data, and then perform PCA and K-means
clustering on the data.
a. Generate a simulated data set with 20 observations in each of three classes (i.e. 60
observations total), and 50 variables.
b. Perform PCA on the 60 observations and plot the first two prin- cipal component
score vectors. Use a different color to indicate the observations in each of the three
classes. If the three classes appear separated in this plot, then continue on to part
(c). If not, then return to part (a) and modify the simulation so that there is greater
separation between the three classes. Do not continue to part (c) until the three
classes show at least some separation in the first two principal component score
vectors. Make sure there is also some overlap between the classes!
c. Perform K-means clustering of the observations with K = 3. How well do the clusters
that you obtained in K-means clustering compare to the true class labels?
d. Perform K-means clustering with K = 2. Describe your results.
e. Now perform K-means clustering with K = 4, and describe your results.
f. Now perform K-means clustering with K = 3 on the first two principal component
score vectors, rather than on the raw data. That is, perform K-means clustering on
the 60 × 2 matrix of which the first column is the first principal component score
vector, and the second column is the second principal component score vector.
Comment on the results.
g. Using the scale() function, perform K-means clustering with K = 3 on the data after
scaling each variable to have standard deviation one. How do these results compare
to those obtained in (c)? Explain.

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