1 Objective Question
What are the objectives of Principal Components Analysis (PCA)? Select all that are correct.
- Maximize the variance along the new output dimensions
- Minimize the variance along the new output dimensions
- Maximizing the orthogonal distance between the data and the new outputdimension
- Minimize the orthogonal distance between the data and the new outputdimension
2 Subjective Question
Prove that there exist a relationship between PCA and SVD for a given data matrix X. Explain in one line how will you use the the SVD of the data matrix X to perform dimensionality reduction?
3 Programming Question
Consider the problem of Eigenfaces. Given a dataset of face images, your task is to find a lower dimensional representation by applying PCA. Write a program to output the following:
- How many principal components are required such that 95% of the variance in the data is preserved?
- Show the reconstruction of the first 10 face images using only 100 principalcomponents.
- Show the above two results for a noisy face dataset.