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Consider again the same 1 0 instances. P 1 = ( 4 , 1 ) P 2 = ( 2 , 1 ) P 3

Consider again the same 10 instances.
P1=(4,1)
P2=(2,1)
P3=(2,2)
P4=(5,5)
P5=(3,2)
N1=(3,4)
N2=(1,1)
N3=(3,6)
N4=(3,1)
N5=(2,3)
A neural network comprising of 2 input neurons (for x and y values),2 hidden layer neurons (h1 and
h2), and a single output neuron, was trained to classify the data. The hidden and output neurons use
the threshold activation function, which outputs either 0(for a negative instance) or 1 for a positive
instance.
y
x
h2
h1
o1
wh2
2=1
wh1
2=-1
wh2
1=3
wh1
1=1
wo1
2=2
wo1
1=2
wh2
0=-3
wh1
0=1
wo1
0=-3
Figure 3: Three-layer neural network with weights and bias values.
6
COS4852/A2
i) Calculate the output for each of the three neurons h1, h2, and o1 when N3 is given as input to
the network. Use the weights and bias values as shown in Figure 3.
ii) Does the network classify N3 correctly?
iii) What do you observe about the outputs of h1 and h2 when N3 is given as input? Could the
network still correctly classify N3? Explain in detail.
iv) Draw the decision boundaries for each of the three neurons, h1, h2, and o1. Show all your
steps and calculations. Explain what you did to arrive at the diagram for o1.

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