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Question 1 : An artificial neuron with linear activation function, two inputs and a bias is trained using the rules: w t + 1 =

Question 1: An artificial neuron with linear activation function, two inputs and a bias is
trained using the rules:
wt+1=wt+xt, if xt belongs to class-1 and the transpose of wt multiplied
with xt is less than or equal to zero;
wt+1=wt-xt, if xt belongs to class-2 and the transpose of wt multiplied
with xt is greater or equal to zero;
wt+1=wt otherwise.
In the above expressions, w is the weight vector, t denotes iterations, and x is the feature vector
as shown in the following table:
All weights are zero at the start, i.e.w0=[0,0,0]T, where T indicates the transpose of the
vector, the first zero element in this vector is the initial weight of the first input x1, the second
zero is the initial weight of the second input x2, and the last zero element in this vector is the
weight of the bias term, which always receives an input equal to 1. The neuron is trained by
feeding input vectors in the order presented in the table, i.e.t=0,1,2,3. For example, starting
from the top, at t=0, the first input pattern is -1,0 and the correct classification for this input
vector is "class-1".
(Q1.1) What would the weights be after the presentation of each one of the input patterns?
Show and explain all your calculations.
(10 marks)
(Q1.2) What would the weights be if you continue training for three more iterations, i.e.
t=4,5,6? Show and explain your calculations. What is the weight vector at the end of training
(t=6)? Show and explain all your calculations.
(10 marks)
(Q1.3) Has the training algorithm reached convergence at t=6? Explain your view. What is the
equation of the line that defines the decision boundary of this neuron at t=6? Show and explain
all your calculations.
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