Problem
Complete the following experiments using MATLAB or GNU Octave. Write code to implement both PCA and whitening-you can use functions such as eig or svd, but do not use functions that directly complete the task for you (e.g., the princomp function).
i. Generate 2000 examples using x=randn(2000,2)*[2 1;1 2], in which the examples are two-dimensional. Use the scatter function to plot these 2000 examples.
ii. Perform the PCA operation on these examples and keep both dimensions. Use the scatter function to plot the examples after PCA.
iii. Perform the whitening operation on these examples and keep both dimensions. Use the scatter function to plot the examples after PCA.
iv. Why is PCA a rotation (after the translation operation) of the data if all dimen- sions are kept in the PCA operation? Why is this operation useful?