Out of three genetic operators viz. selection, cross-over and mutation, list and justify which operator or combination there of will be required for the following:
i) To fill the population with copies of the best individual from the population.
ii) For the convergence of an algorithm to good but sub-optimal solution.
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Consider a dataset of five observations given in the following table, each of which has two features f1 and f2:
| x₁ | x₂ | x₃ | x₄ | x₅ | |
|---|---|---|---|---|---|
| f₁ | 2 | 3 | 4 | 3 | 5 |
| f₂ | 6 | 7 | 5 | 4 | 6 |
Assume the number of cluster and the real number
. Also, assume the initial cluster centers as
and
. Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.
State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) 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.
b) The length of chromosomes to determine the maximum value of the set:
is 12.
c) The fuzzy relation (R) given below, is an equivalence relation.
d) The Self Organizing Map (SOM) is a supervised learning technique.
e) In a single layer neural network, if , then the output is -1.
A single layer neural network is to have six inputs and three outputs. The outputs are continuous over the range 0 to 1. Now answer the following:
i) How many neurons are required?
ii) What are the dimensions of the weight matrix?
iii) What kind of transfer function could be used?
iv) Is a bias required? Give reasons.
Using diagram, show the difference between feed-forward neural network and recurrent neural network.
Consider the fuzzy sets A and B defined on the interval [0, 5]. Their membership functions are:
$
and
Determine the membership function and graph them for each of the following:
i) AC, BC
ii)
iii)
iv)
v)
Find the length and order of the following schema:
i)
ii)
iii)
iv)
Consider the ADALINE filter with three neurons in the input layer having weights 3,1 and − 2and the input sequence ......., ,0,0,0 − 0,0,0,5,4 ,.....}. Find the filter output.