Computer the output for the neurons in the kohonen networks, the related data is given below:
i) Input to Kohnen neural network:
Input Neuron-1` (I1) =0.5
Input Neuron-2 (I2) =0.75
ii) Connected weights between the neurons are as given below:
I O 1.0:
1 → 1
I O 2.0:
2 → 2
I O 3.0:
1 → 2
I O 4.0
Kohonen neural networks, also known as self-organizing maps (SOMs), are a type of artificial neural network used for unsupervised learning tasks, particularly in clustering and pattern recognition. In a Kohonen network, neurons organize themselves in a 2D grid and are responsive to certain ________ ____ ____ ____ ______.
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Generate the population in the next iteration by using Roulette-Wheel criterion:
| k | Fk |
| 1 | 3.5 |
| 2 | 4.6 |
| 3 | 5 |
| 4 | 2.8 |
| 5 | 1.8 |
State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) The length of chromosomes to determine the maximum value of the set:
S ={X 0 ≤x ≤ 4096}is 12.
b) In the Hopfield network, the neurons belonging to the same layer receive input from
the neurons of the previous layer and send their value only to the neurons of the next
layer.
c) In a single layer neural network, if x ,0
ω > then the output is −1.
d) The fuzzy relation (R) given below, is an equivalence relation.
e) The Self Organizing Map (SOM) is a supervised learning technique.
Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:
f(x) =
Subject to:
1≤ x ≤16
Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.
Consider the two parents which are participating in partially mapped cross over as shown below:
Parent 1: C D | E A B |I H G F
Parent 2: A B | C D E |F G H I
Using partially mapped crossover assuming 2nd and 6th as the cross over sites, find the children solution.
Consider a dataset of five observations given in the following table, each of which has two features f and f 2:
Assume the number of cluster c = 3 and the real number m = 2 . Also, assume the initial cluster centers as V )1,1( 1 = and V )2,2( 2 = . Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.
Implement AND function using McCulloch-Pitts neuron.
Consider the single layer perception given below:
Obtain the output for each of the following input pattern:
| Patterns | p1 | p2 | p3 | p4 |
| x1 | 1 | 0 | 1 | 1 |
| x2 | 0 | 1 | 0 | 1 |
| x3 | 0 | 1 | 1 | 1 |