ECE
5120
Homework Assignments
(Click on links below to view solutions in
pdf format)
HW #1; Chapter #1: {1.1.1, 1.1.2, 1.2.2,
1.2.4, 1.3.5, 1.3.7(a), 1.4.1}
HW #2; Chapter #2: {2.1.1, 2.1.2, 2.1.3,
2.2.2}
HW #3; Chapter #3: {3.1.3, 3.1.4}. Also,
solve the following four problems:
I. Employ
the Perceptron learning rule (given in Equation 3.1.3, p. 60),
with w^{1}
= 0, to synthesize a separating surface for the mapping defined below.
Assume
that the order of training sample presentation is preserved, as in the
table
below. Plot the separating surface.
x_{1} |
x_{2} |
d |
0 |
1 |
-1 |
1 |
0 |
-1 |
1 |
1 |
1 |
.5 |
1 |
1 |
II.
Given the function F(x) = x^{4} - (2/3)x^{3}
- 2x^{2} + 2x + 4
a. Find all stationary points.
b. Identify all minima, maxima, and
saddle points.
c. Identify the global minimum.
III.
Consider the following function: F(x_{1},x_{2})
= (x_{2} - x_{1}) ^{4} + 8x_{1}x_{2}
- x_{1} + x_{2} + 3.
a. Find the second order Taylor series
expansion of F.
b. Find all stationary points.
c. Test these points for local minimum.
d. Verify the local minima by plotting
the function.
IV.
Consider the function J(w_{1},w_{2}) =
-(1/4)w_{1}^{2} -(3/2)w_{1}w_{2}
-(1/4)w_{2}^{2}.
a. Find the eigenvalues and eigenvectors
of the Hessian of J.
b. Generate 3-D plot for J and its
contour plot (you may use Matlab).
c. Display the direction of the
eigenvectors on the contour plot.
HW #4; Chapter#3: {3.1.6, 3.3.1, 3.3.2,
3.4.2} Note: for problem 3.1.6
modify
the problem to replace Butz's rule by the Perceptron learning rule with
learning
rate of 0.05.
HW #5; Chapter #4: {4.3.3, 4.3.7, 4.3.9
(Oja's Rule only), 4.4.1}
HW #6; Chapter #5: {5.1.1, 5.1.2, 5.1.3,
5.1.4, 5.1.5, 5.1.7}
HW #7; Chapter #6: {6.1.1, 6.1.7, 6.1.8}