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Gujarat Technological UniversityWinter 2025 Examination

GTU 3171613 Pattern Recognition Winter 2025 Paper Solution & PDF

B.E. · IT Engineering · Semester 7 · Subject Code: 3171613
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Total Marks70 MarksExternal theory exam
Passing Marks23 Marks33% minimum cutoff
Exam Duration2.5 Hours10:30 AM – 1:00 PM
Paper Structure5 QuestionsWith internal OR choices
Jump toQ1Q2Q3Q4Q5

Question 1

14 MarksMedium
(a)

Define the following terms: conditional probability, joint probability and independent events.

3 Marks
(b)

Find inner product and outer product of following two vectors U and V, where U = [2 7 5 6] and V = [4 1 7 2]

4 Marks
(c)
(
1)Suppose we are rolling a fair dice. The possible outcomes are 1, 2, 3, 4, 5 and 6. Let random variable X represent the outcomes. Calculate the expected value of X i.e E[X] ?
2)Suppose a bag has total 10 balls. Out of 10 balls, 6 are red, 3 are blue and 1 is green. Consider following events A and B. Calculate conditional probability P(A|B). Event A: Drawing a red ball from the bag. Event B: Drawing a ball that is not green.
3)Define : Autocorrelation
7 Marks

Question 2

14 MarksMedium
(a)

State for each problem, whether it belongs to supervised learning or unsupervised learning or none of the two ?

1Predict decease from blood sample
2Group audio files based on language of speakers
3Face Recognition to unlock mobile phone
4Predict sales of a product
5Group applicants for a job as per their nationality
6Learning to play chess
3 Marks
(b)

Consider two class classification problem. The classes are denoted as w1 and w2. Apply Baye’s minimum risk classification rule to decide whether sample x belongs to class w1 or w2. Use the following data: P(w1) = 0.6, P(w2) = 0.4, P(x) = 0.74, P(x|w1) = 0.75, P(x|w2) = 0.4. Loss parameters are: λ11 = 0.3, λ12 = 0.7, λ21 = 0.65, λ22 = 0.35.

4 Marks
(c)

[1] Explain the two types of states in Hidden Markov Model. [2] Explain the two types of probabilities in Hidden Markov Model. [3] Explain step by step Hidden Markov Model Algorithm.

7 Marks
OR OPTION
(c)
Discus concept of Gaussian Mixture Model.
7 Marks

Question 3

14 MarksMedium
(a)

Assume marks obtained by students in an examination follows normal distribution. The marks obtained are : 40, 45, 50, 30, 55, 70, 83, 90, 25, 66. Find parameters of normal distribution using Maximum Likelihood Estimation.

3 Marks
(b)
Explain with an example why large dimension of dataset is not desirable ?
4 Marks
(c)

Consider the below given two dimensional dataset with two features X1 and X2. Group the records into clusters using Single Linkage Hierarchical clustering and draw the dendogram. Use Euclidean distance. Sr. No. X1 X2 S1 4 3 S2 1 4 S3 2 1 S4 3 8 S5 6 9 S6 5

7 Marks
OR OPTION
(a)
What do you mean by parameter estimation ? Explain Bayesian estimation.
3 Marks
(b)

Compare Principal Component Analysis and Fisher’s Linear Discriminant Analysis.

4 Marks
(c)

Consider the following dataset of age and salaries of employees. Apply K-Means clustering algorithm to divide data into TWO clusters. Start with employee E1 as centroid of first cluster and E2 as centroid of the second cluster. Use Euclidean distance. Employee code Employee Age Salary E1 20 500 E2 40 1000 E3 30 800 E4 18 300 E5 28 1200 E6 25 1400 E7 35 1800

7 Marks

Question 4

14 MarksMedium
(a)
Discuss working of MP (McCullochh Pitts) neuron.
3 Marks
(b)
Explain following two activation functions used in neural networks:
1)Sigmoid
2)Tanh
4 Marks
(c)
Write and explain Perceptron learning algorithm.
7 Marks
OR OPTION
(a)
Discuss working of classical Perceptron.
3 Marks
(b)

Explain following two activation functions used in neural networks:

1)RELU
2)Softmax
4 Marks
(c)
Explain gradient descent algorithm for learning neural network parameters.
7 Marks

Question 5

14 MarksMedium
(a)
Discuss idea of convolution operation with an example.
3 Marks
(b)
Discuss various types of non-numeric/notional data.
4 Marks
(c)
Explain working of SVM.
7 Marks
OR OPTION
(a)

Discuss idea of pooling operating used in Convolutional Neural Networks (CNNs) with an example.

3 Marks
(b)
Explain working of Recurrent Neural Networks (RNN).
4 Marks
(c)
Explain working of Classification and Regression Trees.
7 Marks
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About this Examination Paper & Attribution

Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Pattern Recognition (Winter 2025, B.E. · IT Engineering, Sem 7). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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