GATE DA Machine Learning – Full Mock Test-1

Questions 61-65 of 100

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Question 61

MSQ · Multiple Correct 2 mark

Which of the following statements regarding EXPECTATION-MAXIMIZATION (EM) for GMMs are CORRECT?

A The E-step computes posterior responsibilities gamma_ik using the current parameter estimates. B The M-step updates means, covariances, and mixing weights by maximizing the expected log-likelihood. C EM is guaranteed to monotonically increase (or hold constant) the observed log-likelihood at every iteration. D EM is guaranteed to find the global optimum log-likelihood.

Question 62

MSQ · Multiple Correct 2 mark

Which of the following dimensionality reduction techniques perform NON-LINEAR feature mapping or manifold learning?

A Kernel PCA B t-SNE C ISOMAP D Standard PCA

Question 63

NAT · Numerical Answer 2 mark

A 3x3 covariance matrix has eigenvalues lambda_1 = 6.0, lambda_2 = 3.0, and lambda_3 = 1.0. What fraction of total variance is retained if we reduce the dataset to 2 principal components? (Round to 2 decimal places)

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Question 64

NAT · Numerical Answer 2 mark

In a dataset of 100 samples, sample x_i has average intra-cluster distance a(i) = 2.0 and minimum average nearest-cluster distance b(i) = 6.0. What is the Silhouette Coefficient s(i) for sample $x_i$? (Round to 2 decimal places)

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Question 65

NAT · Numerical Answer 2 mark

In LDA for a 4-class problem (C = 4) with 100-dimensional feature vectors (d = 100), what is the maximum number of discriminant directions that can be extracted?

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