6. Data-Driven Methods

Dimensionality Reduction — Quiz

Test your understanding of dimensionality reduction with 5 practice questions.

Practice Questions

Question 1

Which dimensionality reduction technique is most appropriate for unwrapping a Swiss roll manifold to a lower-dimensional embedding?

Question 2

Given singular values $\{4,3,2,1\}$ from the SVD of a centered data matrix, what fraction of the total variance is captured by the first two modes?

Question 3

Which of the following expressions gives the optimal rank-$k$ approximation $X_k$ of a matrix $X$ in the Frobenius norm, given its SVD $X=U\Sigma V^T$?

Question 4

In Locally Linear Embedding (LLE), what is the primary objective when computing the reconstruction weights $w_{ij}$?

Question 5

Which eigen-decomposition does Kernel PCA perform to find principal components in the feature space?