Problem 1 [33%]
Describe, in words, the results that you would expect if you performed K-means clustering of the eight shoppers in Figure 10.14 in ISL, on the basis of their sock and computer purchases, with K = 2. Give three answers, one for each of the variable scalings displayed. Explain.
Problem 2 [33%]
In this problem, you will compute principal components for the Auto dataset. First remove qualitative features, which cannot be handled by PCA. Then:
1. Compute principal components without scaling features. Plot the result (you can use ggfortify::autoplot).
2. Compute principal components after scaling features to have unit variance. Plot the result (you can use ggfortify::autoplot).
3. How do the principal components computed in parts 1 and 2 compare?
Problem 3 [33%]
1. Apply PCA to a subset of the MNIST dataset. Plot the first few principal vectors. Describe what you observe and interpret the results.
2. Optional(+10 points): Apply k-means clustering to the MNIST dataset both with the original features, and using at least two different subsets of the principal components. Which approach works best? Explain.
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