EE-538: NEURAL NETWORKS
HOMEWORK 3
MARYAM ASAD
STUDENT ID: 20225384
SCHOOL OF EE
KAIST
Homework 3
Question 1
Given at end handwritten.
Question 2
Used Platform: MATLAB
Part b of Homework 2 Question 2 by Homework 2 algorithm
The homework 2 algorithm was the algorithm on last slide of lecture 2. It did not include any normalization
therefore the weight vector and thus y grew very large. The data for pat b of question 2 (N1=0, N2=200,
N3=200) is shown in figures 1 and 2; in 2D and 3D respectively. The first principal component obtained from
this algorithm is shown in figure 3.
Figure 1
Figure 2
Figure 3
Part b of Homework 2 Question 2 by Homework 3 algorithm
The same question with same data is solved by algorithm with normalization on slide 3-3 of lecture 3. The
principal component thus obtained is shown in figure 4. The y axis shows smaller values as compared to that
of algorithm without normalization. However, in both cases it remains finite. The weight vector for algorithm
without normalization has larger magnitude than that of without normalization.
Figure 4
Part d of Homework 2 Question 2 by Homework 2 algorithm
The data for part d of question 2 (N1=0, N2=200, N3=200) is shown in figures 5 and 6; in 2D and 3D
respectively. The first principal component obtained from this algorithm is shown in figure 7. The homework
2 algorithm was the algorithm on last slide of lecture 2. It did not include any normalization therefore the
weight vector and thus y grew very large as shown in figure 7.
Figure 5
Figure 6
Figure 7
Part d of Homework 2 Question 2 by Homework 3 algorithm
The same question with same data is solved by algorithm with normalization on slide 3-3 of lecture 3. The
principal component thus obtained is shown in figure 8. The y axis shows smaller values as compared to that
of algorithm without normalization in figure 7. However, in both cases it remains finite. The weight vector for
algorithm without normalization has larger magnitude than that of without normalization.
Figure 8
Question 3
Part a
The generated data is as follows in figures 9 and 10 in 2D and 3D respectively. N1=N2=300 and c1=c2=1.
Figure 9
Figure 10
Part c
The generated data is as follows in figures 11 and 12 in 2D and 3D respectively. N1=N2=300 and c1=1, c2=2.
Figure 11
Figure 12
Part e
The generated data is as follows in figures 13 and 14 in 2D and 3D respectively. N1=200, N2=300 and
c1=c2=1
Figure 13
Figure 14
Part b
The decision boundary by Single Layer Perceptron is shown in figure 15. N1=N2=300 and c1=1, c2=1. Eta is
0.0005 for all parts.
Figure 15
Part d
The decision boundary by Single layer perceptron is shown in figure 16. Standard deviation of B is greater
than class A hence B are more spread out. N1=N2=300 and c1=1, c2=2
Figure 16
Part f
The decision boundary by Single layer perceptron is shown in figure 17. Red dots are less because they are
20 while blue are 300. N1=200, N2=300 and c1=c2=1
Figure 17