## NPTEL Computer Vision Week 10 Assignment Answers 2024

1. Which of the following statements are true for an Artificial Neural Network?

a) A single neuron with two inputs and the signum activation function can implement an AND gate.

b) A single neuron with two inputs and the signum activation function can implement an XOR gate.

c) A single neuron with multiple inputs and the signum activation function acts as a linear discriminator in a multidimensional feature space for two linearly separable classes.

d) A single neuron with multiple inputs and the sigmoid activation function computes posterior of a class for a two-class classification problem in a multidimensional feature space.

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2. Consider the following table. The table shows the points on x-axis and its corresponding class.

Point | Class |

2.5 | 1 |

3.5 | 2 |

4.0 | 1 |

5.0 | 2 |

5.5 | 2 |

We introduce two new points on x-axis, 3.7 and 4.2. Compute KNN (K=3) to determine their class.

a) 3.7 : Class 2 and 4.2: Class 1

b) 3.7 : Class 1 and 4.2: Class 2

c) 3.7 : Class 1 and 4.2: Class 1

d) 3.7 : Class 2 and 4.2: Class 2

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3. Assume, you have 5 types of objects with 3 attributes each as shown in the table. Consider object A and object C as the initial centroids.

Object | Attribute 1 | Attribute 2 | Attribute 3 |

A | 1 | 1 | 1 |

B | 2 | 1 | 2 |

C | 5 | 3 | 2 |

D | 4 | 4 | 0 |

E | 3 | 1 | 3 |

What will be the elements in each clusters after the first iteration?

a) Cluster 1: A, B, E Cluster 2: C, D

b) Cluster 1: A, B Cluster 2: C, D, E

c) Cluster 1: A, E Cluster 2: B, C, D

d) Cluster 1: A, C Cluster 2: B, D, E

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4. The output of a neural network is [2, 4, 7, 1, 5]. Find the softmax probability for 7. Answer to 4 places of decimals.

Answer :-

5. Assume, you want to cluster 7 observations into 3 clusters using K-Means clustering algorithm. After first iteration clusters, C1, C2, C3 has following observations:

C1: (2,2), (4,4), (6,6)

C2: (0,4), (4,0)

C3: (5,5), (9,9)

What will be the cluster centroids if you want to proceed for second iteration?

a) C1: (4,4), C2: (2,2), C3: (7,7)

b) C1: (6,6), C2: (4,4), C3: (9,9)

c) C1: (2,2), C2: (0,0), C3: (5,5)

d) C1: (2,2), C2: (0,4), C3: (5,5)

Answer :-

Consider the following neural network. Ix : Inputs; Bx : Biases; Hx : Hidden Layers; Ox :Outputs. If all the Activation Functions are ReLU, then answer the following question 6 and 7:.

6. What will be the output for Input [1, 1]?

a) O1 : 0, O2 : 0

b) O1 : 0, O2 : 1

c) O1 : 1, O2 : 0

d) O1 : 1, O2 : 1

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7. What will be the output if sigmoid activation functions are used in the output layer instead of ReLU? Note: Hidden layer still has ReLU.

a) O1 : 0.731, O2 : 1

b) O1 : 0.731, O2 : 0.731

c) O1 : 0.5, O2 : 0.5

d) O1 : 1, O2 : 0.731

Answer :-

8. Consider a multilayer feed forward network which takes a 10-D feature vector as input and produces a 2-D output vector. The network has one hidden layer with number of neurons 15. Please note that the input vector is the input to the first hidden layer. What is the dimension of the parametric space over which the optimization process would be carried out to train the network?

Answer :-

9. We want to classify whether a special wire is good or not. Consider the following table consisting of four samples.

Durability | Strength | Label |

7 | 7 | bad |

7 | 4 | bad |

3 | 4 | good |

1 | 4 | good |

We introduce a new wire with durability 3 and strength 7. Which of the following statements are true after computing KNN (K=3)?

a) (3, 7) is a bad wire.

b) The nearest sample to (3, 7) is at a distance of 4.

c) (3, 7) is a good wire.

d) The nearest sample to (3, 7) is at a distance of 3.

Answer :-

10. Calculate cosine similarity between [7, 4, 8, 2] and [3, 21, 5, 1].

a) 0.5842

b) 0.4872

c) 0.2314

d) 0.0950

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