Are you looking for the Deep Learning IIT Ropar Week 5 NPTEL Assignment Answers 2024 (July-Dec)? You’ve come to the right place! Access the most accurate and up-to-date solutions for your Week 5 assignment in the Deep Learning course offered by IIT Ropar.
Which of the following is the most appropriate description of the method used in PCA to achieve dimensionality reduction? A. PCA achieves this by discarding a random subset of features in the dataset B. PCA achieves this by selecting those features in the dataset along which the variance of the dataset is maximised C. PCA achieves this by retaining the features in the dataset along which the variance of the dataset is minimised D. PCA achieves this by looking for those directions in the feature space along which the variance of the dataset is maximised View Answer
What is/are the limitations of PCA? A. It can only identify linear relationships in the data. B. It can be sensitive to outliers in the data. C. It is computationally less efficient than autoencoders D. It can only reduce the dimensionality of a dataset by a fixed amount. View Answer
The following are possible numbers of linearly independent eigenvectors for a 7×7 matrix. Choose the incorrect option. A. 1 B. 3 C. 9 D. 5 E. 8 View Answer
Find the singular values of the following matrix: [−43−6−8] A. σ1 = 10, σ2 = 5 B. σ1 = 1, σ2 = 0 C. σ1 = 100, σ2 = 25 D. σ1 = σ2 = 0 View Answer
PCA is performed on a mean-centred dataset in R³. If the first principal component is 16√(1, −1, 2), which of the following could be the second principal component? A. (1, −1, 2) B. (0, 0, 0) C. 15√(0, 1, 2) D. 12√(−1, −1, 0) View Answer
What is the mean of the given data points x1, x2, x3? A. [11] B. [1.67] C. [2] D. [0.33] View Answer
The covariance matrix C = 1/n Σ (x − x̄)(x − x̄)T is given by: (x̄ is mean of the data points) A. [8.66 −7.33; −7.33 8.66] B. [2.88 −2.44; −2.44 2.88] C. [0.22 −0.22; −0.22 0.22] D. [5.33 −5.33; −0.33 0.33] View Answer
The maximum eigenvalue of the covariance matrix C is: A. 1 B. 5.33 C. 0.44 D. 0.5 View Answer
The eigenvector corresponding to the maximum eigenvalue of the given matrix C is: A. [1, 1] B. [−1, 1] C. [0.670] D. [−1.481] View Answer
Given that A is a 2×2 matrix, what is the determinant of A, if its eigenvalues are 6 and 7? View Answer
1. Which of the following is a measure of the amount of variance explained by a principal component in PCA?
a) Covariance b) Correlation c) Mean absolute deviation d) Eigenvalue
Answer:d) Eigenvalue
2. What is/are the limitations of PCA?
a) It is computationally less efficient than autoencoders b) It can only reduce the dimensionality of a dataset by a fixed amount. c) It can only identify linear relationships in the data. d) It can be sensitive to outliers in the data.
Answer:d) It can be sensitive to outliers in the data.
3. Which of the following is a property of eigenvalues of a symmetric matrix?
a) Eigenvalues are always positive b) Eigenvalues are always negative c) Eigenvalues are always real d) Eigenvalues can be complex numbers with imaginary parts non-zero
Answer:c) Eigenvalues are always real
4. The eigenvalues of A are 3, 4. Which of the following are the eigenvalues of A³?
a) 3, 4 b) 9, 16 c) 27, 64 d) √3, √4
Answer:b) 9, 16
5. If we have a 12×12 matrix having entries from R, how many linearly independent eigenvectors corresponding to real eigenvalues are possible for this matrix?
a) 10 b) 24 c) 12 d) 6
Answer:c) 12
6. What is the mean of the given data points x₁, x₂, x₃?
a) [5.5] b) [1.67, 1.67] c) [2.2] d) [1.5, 1.5]
Answer:b) [1.67, 1.67]
7. The covariance matrix C=1/n ∑(x−x̄)(x−x̄)T is given by:
a) [0.22, −0.11; −0.11, 0.22] b) [0.33, −0.17; −0.17, 0.33] c) [0.22, −0.22; −0.22, 0.22] d) [0.33, −0.33; −0.33, 0.33]
Answer:a) [0.22, −0.11; −0.11, 0.22]
8. The maximum eigenvalue of the covariance matrix C is:
a) 0.33 b) 0.67 c) 1 d) 0.5
Answer:d) 0.5
9. The eigenvector corresponding to the maximum eigenvalue of the given matrix C is:
a) [0.71, 0.71] b) [−0.71, 0.71] c) [−1, 1] d) [1, 1]
Answer:a) [0.71, 0.71]
10. What is the determinant of a 2×2 matrix that has eigenvalues of 4 and 5?
Answer: 20
These are Deep Learning IIT Ropar Week 5 Nptel Assignment Answers
