Describe the Binary Hopfield network with the help of an example.
The Binary Hopfield Network is a type of recurrent artificial neural network used in soft computing and applications such as pattern recognition, optimization, and associative memory. It was introduced by John Hopfield in the 1980s and is characterized by its simplicity and capacity to store and retrieve binary patterns.
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a) The input to a single input neuron is 2, its weight is 2.3 and its bias is - 3 . The neuron output for Linear transfer function is -1 .
b) The SOM is useful for classification.
c) Gradient based optimization methods are used when the objective function is not smooth and one needs efficient local optimization.
d) The -cut of a fuzzy set A in
is defined as A
. {x
A (x)
0 }.
e) If W (k0) = W (k0 +1 (k0 + 2) , then perceptron is non-linear separable.
Use a binary-coded Genetic algorithm (GA) to minimize the function f ( x1 , x2 ) = x1+ x2 + 2x12- x22+ x1 , x2, in the range of 0 x1, x2
5 . Use a random population of size N = 6 , a single point crossover with probability Pc=1 and neglect mutation. Assume 3 bits for each variable and thus the GA-string will be 6- bits long. Show only one iteration by hand calculation.
Find max-average composition for R ( x , y ) and S ( x , y ) defined by the following relational matrices:
Write any three terminating conditions used in learning of a neural network.
Let an activation function be defined as , . Show that
What is the value of
( v ) at the origin? Also, find the value of
as v approaches +
and -
.
Consider the problem of finding the shortest route through several cities, such that each city is visited only once and in the end traveler returns to the starting city (the travelling salesman problem). Suppose that in order to solve this problem we use a genetic algorithm, in which genes represent links between pairs of cities. For example, a link between Delhi and Mumbai is represented by a single gene DM : Also assume that the direction in which we travel is not important, so that DM = MD .
i) How many genes will be used in a chromosome of each individual if the number of cities is 10?
ii) How many genes will there be in the alphabet of the algorithm?
Define the following operations in Genetic algorithm with one example of each
i) Crossover
ii) Mutation