IITM MLT Week 1 Questions
Principal Component Analysis (PCA)
Week 1 question PDF
Practice dimensionality reduction using principal components, eigenvalues and projections. The collection includes numerical questions about variance, reconstruction and the relationship between the data matrix and its Gram matrix.
The complete question statements, options, numerical data and any supporting graphs or tables are in the PDF. Numbered comprehension questions can include several subquestions. Answer keys are included for checking your attempt; these are not full worked solutions.
Topics covered in this collection
- Principal components and orthogonality
- Eigenvalues and explained variance
- Projection and reconstruction error
- PCA through the Gram matrix
How to approach these questions
- Check that the data is centered before interpreting covariance and principal components.
- Keep track of whether eigenvectors belong to the covariance matrix or the Gram matrix; the normalization is different.
- For reconstruction questions, project onto the retained components before calculating the residual.
Attempt the questions using the assumptions and notation stated in each problem. For short-answer questions, round only at the final step to the requested precision. Check the provided key after solving and revisit the relevant concept when an answer differs.