## Implement the support vector machine algorithm

?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), Jp(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 yk is misclassified by a then a ← a + yk?

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 Yk = {}

4 j ← 0

5 do j ← j + 1

6 if aryj ≤ b then Append yj to Yk

7 until j = n

8 a ← a + η(k)Σy∈Y b-aty/||y||2Y

9 until Yk = {}

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)(bk – atYk)Yk

4 until |η(k)(bk – atyk)yk| < 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.