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MLT · PCA, kernel PCA & kernels

17 questions · 46 marks · 7 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Machine Learning Techniques

PCA, kernel PCA & kernels

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1MSQ4 Marks·Choose all correct options
Key ↓
1. AThere will be 50 non-zero eigenvalues of the covariance matrix.
2. BThere will be 6 non-zero eigenvalues of the covariance matrix.
3. CUsing the first 5 principal components, the dataset can be reconstructed with zero residue.
4. DThe variance captured by the top 6 principal components equals the total variance of the dataset.
Q2MSQ3 Marks·Choose all correct options
Key ↓
Which of the following are valid kernel functions? Select all that apply.
1. A
2. B
3. C
4. D
Q3NAT3 Marks·Write the number
Key ↓
Your answer:
Q4NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q5–Q7
Based on the above data, answer the given subquestions.
Q5MCQ2 Marks·Choose one option
Key ↓
What is the covariance matrix of the dataset?
1. A
2. B
3. C
4. D
Q6NAT2 Marks·Write the number
Key ↓
If standard PCA is performed on this dataset, what is the variance along the first principal component? Enter the answer correct to one decimal place.
Your answer:
Q7NAT2 Marks·Write the number
Key ↓
If standard PCA is performed on this dataset, what is the variance along the second principal component? Enter the answer correct to one decimal place.
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Q8MCQ3 Marks·Choose one option
Key ↓
1. APCA has reduced the dimensionality of the dataset because the combinations of features are de-correlated.
2. BPCA has not reduced the dimensionality of the dataset because all principal components are retained.
3. CPCA always reduces the dimensionality of the dataset regardless of the number of components retained.
4. DPCA can never be used for dimensionality reduction.
Q9MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D

End Term · 31 Aug 2025 (AN)End Term

Q10MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q11NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q12MSQ3 Marks·Choose all correct options
Key ↓
Which of the following statements correctly differentiates PCA and Kernel PCA?
1. APCA maximizes variance in the original feature space, while Kernel PCA maximizes variance in a higher-dimensional transformed space.
2. BPCA finds principal components using linear transformations in the original space, while Kernel PCA uses non-linear transformations to find principal components in a higher- dimensional space.
3. CKernel PCA can capture non-linear patterns in data, making it useful when PCA fails to represent complex structures in a linear space.
4. DPCA and Kernel PCA always yield identical results regardless of the dataset structure.

End Term · 13 Apr 2025 (AN)End Term

Q13MCQ2 Marks·Choose one option
Key ↓
1. AKernel PCA with a polynomial kernel of degree 2.
2. BKernel PCA with a polynomial kernel of degree 3.
3. CKernel PCA with a polynomial kernel of degree 4.
4. DStandard PCA

End Term · 22 Dec 2024 (FN)End Term

Q14NAT2 Marks·Write the number
Asked 2 times Key ↓
NOTE: Enter the answer correct to one decimal place
Your answer:
Q15NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Q16NAT2 Marks·Write the number
Asked 2 times Key ↓
NOTE: Enter the answer correct to one decimal place
Your answer:
Q17NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1B, D

Q2A, B, D

Q33

Q40.45 to 0.5

Q5B

Q64.5

Q70.5

Q8B

Q9C

Q10C

Q116

Q12A, B, C

Q13B

Q142.5

Q150

Q162.5

Q170

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