Write a program to implement the support vector machine

Question

Question 1:

I want this assignment in Matlab.

?Let patterns y1 = (-1,0) and y2 = (0,0.5) be assigned class I, and pattern y3=(1,0) be assigned class 2. Plot criteria J (a; y1, y2, y3), J_p(a; y1, y2, y3) (Eq. 16, page 227), Js(a; y1, y2, y3) (Eq. 33, page 235) and JA(a; y1, y2, y3) (Eq. 43, page 240), where y1, y2 and y3 are augmented feature vector (Eq. 10, page 222), and a is a weight vector. (You can use "image" in R, "image:icor in MATLAB or Imshow" in Python.) Implement Algorithm 4 (page 230), Algorithm 9 (page 236) and Algorithm 10 (page 246). Plot intermediate weights Lion the corresponding criterion (J) images, starting from a_1.0 = 0

Algorithm 4 (page 230)

Algorithm 4. (Fixed-ineretnent Single-Sample Pereeptron)

1 begin initialize a, k 4- 0

2                    do k ← (k + 1) mod n

3                          if y^k is misclassified by a then a ← a + y^k?

4 until all patterns properly classified

5 return a

6 end

Algorithm 8. (Batch Relaxation with Margin)
1 begin initialize a, η(.), b. k ← 0
2                do k 4- (k 1) mod n
3                Y_k = {}
4                  j ← 0
5                 do j ← j + 1
6 if a^ry^j ≤ b then Append y^j to Y_k

7 until j = n

8 a ← a + η(k)Σ_y∈Y b-aty/||y||²Y

9 until Y_k = {}

10 return a

11 end

Algorithm 10. (LMS)

1. begin initialize a, b, threshold θ, η(.), k ← 0

2. do k ← (k + 1) mod n

3. a ← a + η(k)(b_k - a^tY^k)Y^k

4 until |η(k)(b_k - a^ty^k)y^k| < θ
5 return a

6 end

Question 2:

sample		ω1		ω2		ω3		ω4
	xi	X2	Xi	X2	Xi	X2	Xi	X2
1	0.1	1.1	7.1	4.2	-3.0	-2.9	-2.0	-8.4
2	6.8	7.1	- 1.4	-4.3	0.5	8.7	-8.9	0.2
3	-3.5	-4.1	4.5	0.0	2.9	2.1	-4.2	-7.7
4	2.0	2.7	6.3	1.6	-0.1	5.2	-8.5	-3.2
5	4.1	2.8	4.2	1.9	-4.0	2.2	-6.7	-4.0
6	3.1	5.0	1.4	-3.2	-1_3	3.7	-0.5	-9.2
7	-0.8	-1.3	2.4	-4.0	-3.4	6.2	-5.3	-6.7
8	0.9	1.2	2.5	-6.1	-4.1	3.4	-8.7	-6.4
9	5.0	6.4	8.4	3.7	-5.1	1.6	-7.1	-9.7
10	3.9	4.0	4.1	-2.2	1.9	5.1	-8.0	-6.3

11. Write a program to implement the Support Vector Machine algorithm. Train an SVM classifer with data from to3 and (04 in the following way. Preprocess each training pattern to form a new vector having components 1, x₁, x₂, x₁², x₁x², and x₂².

(a) Train your classifier with just the first patterns in 03 and aht and find the separating hyperplane and the margin.

(b) Repeat part (a) using the first two points in the two categories (four points total). What is the equation of the separating hyperplane, the margin, and the support vectors?

(c) Repeat part (b) with the first three points in each category (six points total), the first four points, and so on, until the transformed patterns cannot be linearly separated in the transformed space.