Quiz6

1.

If \(u_1, u_2, \dots, u_d\) , are eigenvectors (column vectors) of the covariance matrix \(\Sigma\), and \(\lambda_1, \lambda_2, \dots, \lambda_n\) are the eigenvalues, then:

Answer

  • ☐ \(\Sigma = \lambda_1 u_1^T u_1 + \lambda_2 u_2^T u_2 + \dots \lambda_d u_d^T u_d\)
  • ☐ \(\Sigma = \lambda_1 u_1^T + \lambda_2 u_2^T + \dots \lambda_d u_d^T\)
  • ☑ \(\Sigma = \lambda_1 u_1 u_1^T + \lambda_2 u_2 u_2^T + \dots \lambda_d u_d u_d^T\)
  • ☐ \(\Sigma = \lambda_1 u_1 + \lambda_2 u_2 + \dots \lambda_d u_d\)

Question 2

The power method can determine (select the best answer)

Answer

  • ☑ All eigenvalues and eigenvectors by deflation
  • ☐ Eigen value/eigen vector corresponding to second-largest variance
  • ☐ Eigen value/eigen vector corresponding to largest variance
  • ☐ Eigen value/eigen vector corresponding to the smallest variance

Question 3

If \(X^c \in \mathbb{R}^{n \times d}\) is a centered matrix and Σ its covariance matrix, which of the following is PCA?

Answer

  • ☑ \(\Sigma = V\Delta V^T\)
  • ☐ \(X = U\Delta V^T\)
  • ☐ \(\Sigma = U\Delta V^T\)
  • ☐ \(X = V\Delta V^T\)

question 4

If \(X^c \in \mathbb{R}^{n \times d}\) is a centered matrix and Σ its covariance matrix, which of the following is SVD?

Answer

  • ☑ \(X = U\Delta V^T\)
  • ☐ \(\Sigma = U\Delta V^T\)
  • ☐ \(X = V\Delta V^T\)
  • ☐ \(\Sigma = V\Delta V^T\)

Question 5

In Singular Value Decomposition, what does the matrix V represent?

Answer

  • ☑ Eigenvectors of covariance of attributes
  • ☐ Eigenvectors of covariance of data-points
  • ☐ Matrix of eigenvalues on diagonal
  • ☐ Deflated matrix after removing first Principal Component