AKTU MCA Pattern Recognition (BMC033) Question Paper 2025-26

Note: Attempt all Sections. If require any missing data; then choose suitably.

Section A

Q1. Attempt all questions in brief · 2 × 7 = 14 marks

1. List the main components of a pattern recognition system.
2. What is misclassification error?
3. Given the data set X={2, 4, 6, 8}, find the maximum likelihood estimate of the variance.
4. Define Hidden Markov Model .
5. What is non - parametric density estimation?
6. Define agglomerative clustering.
7. What is random initialization in K - means?

Section B

Q2. Attempt any three of the following · 7 × 3 = 21 marks

1. What do you mean by expectation and variance of a random variable? A random variable X has distribution:
   X 1 2 3 4
P(X) 0.1 0.3 0.4 0.2
   Compute:
   (i) Expectation E(X)
(ii) Variance Var(X)
2. Given the prior probabilities and likelihoods:
   P(C1) = 0.7, P(C2) = 0.3
P(x | C1) = 0.5, P(x | C2) = 0.2
   Compute the posterior probabilities P(C1 | x) and P(C2 | x), and determine the final class decision.
3. Explain Fisher Linear Discriminant Analysis in detail.
4. Explain how distance measures affect K - Nearest Neighbors ( KNN ) performance.
5. Compare partitional and hierarchical clustering approaches. P.T.O. P rinted Pages: 2 of 2

Section C

Q3

Attempt any one part of the following · 7 × 1 = 7 marks

1. Given the following observed and expected frequencies:
   Category: A B C
   Observed 10 20 30
Expected 15 15 30
   Find the Chi - square test statistic and state the conclusion at a basic significance interpretation level.
2. Discuss dendrogram representation in hierarchical clustering.

Q4

Attempt any one part of the following · 7 × 1 = 7 marks

1. E xplain different pattern recognition approaches with examples.
2. Given the data points (2, 3), (4, 5), (6, 7), (8, 9) and initial cluster centroids C1=(2, 3) and C2=(8, 9) , perform one iteration of K - means clustering. Determine the cluster assignment for each point and compute the updated (new) centroids for each cluster.

Q5

Attempt any one part of the following · 7 × 1 = 7 marks

1. Given a normally distributed variable with mean μ = 50 and standard deviation σ = 5, an obs erved value x = 60 is recorded. Compute the Z - score for the observation and determine the corresponding probability region under the standard normal distribution.
2. Discuss dimensionality reduction and its importance in pattern recognition.

Q6

Attempt any one part of the following · 7 × 1 = 7 marks

1. Discuss different types of classifiers used in pattern recognition.
2. Describe fuzzy membership functions with examples.

Q7

Attempt any one part of the following · 7 × 1 = 7 marks

1. Given dataset:
   X 2 4 6 8
Y 3 5 7 9
   Compute:
   (i) Mean vector
   (ii) Covariance matrix
   (iii) Eigenvalues and eigenvectors
   (iv) Principal component direction
2. Compare statistical and instance - based learning methods.

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