CS计算机代考程序代写 -4exELEC 400M / EECE 571M Homework 3: Nonlinear Transform -8ex Homework is not handed in. Please solve for your own benefit.

-4exELEC 400M / EECE 571M Homework 3: Nonlinear Transform -8ex Homework is not handed in. Please solve for your own benefit.

ELEC 400M / EECE 571M
Homework 3: Nonlinear Transform

Homework is not handed in. Please solve for your own benefit.

• Exercise 3.11, solution attached

• Exercise 3.13, solution attached

1

• Exercise 3.11

z = Φ(x) = [1, x21, x
2
2]

T : decision boundary is w̃Tz = w̃0 + w̃1z1 + w̃2z2 = 0 in Z and
w̃Tz = w̃0 + w̃1x

2
1 + w̃2x

2
2 = 0 in X

(a) w̃1 > 0, w̃2 < 0: x22 |w̃1| − x 2 1 |w̃2| = − w̃0|w̃1w̃2| This is a hyperbola. -5 -4 -3 -2 -1 0 1 2 3 4 5 x 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 x 2 tilde(w) 0 <0 tilde(w) 0 >0

(b) w̃1 > 0, w̃2 = 0: w̃1x
2
1 + w̃0 = 0 → x1 = ±


− w̃0

w̃1

→ two vertical lines in the (x2, x1)-plane (and w̃0 > 0)

(c) w̃1 > 0, w̃2 > 0, w̃0 < 0: x22 |w̃1| + x21 |w̃2| = − w̃0|w̃1w̃2| > 0
This is an ellipse.

-5 -4 -3 -2 -1 0 1 2 3 4 5

x
1

-5

-4

-3

-2

-1

0

1

2

3

4

5

x
2

(d) w̃1 > 0, w̃2 > 0, w̃0 > 0: |w̃0|+ |w̃1|x21 + |w̃2|x22 = 0
This equation has not solution x1, x2 ∈ R.

• Exercise 3.13

(a) z = [1, x1, x2, x
2
1]

T

2

(b) z = [1, x1, x2, x
2
1, x

2
2]

T

(c) z = [1, x1, x2, x
2
1, x

2
2]

T

(d) z = [1, x1, x2, x
2
1, x

2
2]

T

(e) z = [1, x1, x2, x
2
1, x1x2, x

2
2]

T

(f) z = [1, x1, x2]
T = x

3