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 w1 = 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.

 x1 x2 d 0 1 -1 1 0 -1 1 1 1 .5 1 1

II. Given the function F(x) = x4 - (2/3)x3 - 2x2 + 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(x1,x2) = (x2 - x1) 4 + 8x1x2 - x1 + x2 + 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(w1,w2) = -(1/4)w12 -(3/2)w1w2 -(1/4)w22.

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}