MATH 494: Mathematical Foundations of Machine Learning

Assignment #8

(Due Wednesday, April 17, 2024)

This is the second of the two assignments in unsupervised learning. I believe this one is WAY easier than the deeply traumatic Assignment #7.

You will perform the PCA procedure on a noisy dataset and show that your results are exactly the same as those obtained by sklearn's PCA (and numpy's SVD).

What you need to do:

· Generate exactly the same noisy dataset as you created in Assignment #7.

· Center the dataset (essential!)

· "Perform PCA by hand", that is, use numpy.linalg.eig() to find the eigenvalues and eigenvectors.

· Determine and display the amounts/proportions of variance of the data represented by each principal component.

· Perform PCA with the sklearn's PCA procedure.

· Perform SVD with the numpy's SVD procedure.

· Show that each of the three methods produces virtually identical singular values.