Machine Learning Techniques · IIT Madras BS
IITM MLT Week 2 Questions
Kernels and Kernel PCA
Week 2 question PDF
Explore how kernels represent inner products in a feature space. Work through valid-kernel tests, polynomial feature maps and the dimensions of the matrices used in Kernel PCA.
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
- Valid kernels and symmetry
- Polynomial kernels and feature maps
- Positive semidefinite Gram matrices
- Kernel PCA and feature-space dimensions
How to approach these questions
- Test symmetry before assuming that an expression defines a valid kernel.
- Expand the polynomial kernel and match each term with a coordinate of the feature map.
- Distinguish the number of samples from the dimension of the original or transformed feature space.
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.